Nashville - playing their first season in MLS - had been unable to train ahead of their scheduled opener against Chicago Fire at ESPN's Wide World of Sports Complex.
MLS made the decision to remove the team "in the best interest of the health of all players and staff participating in the tournament", according to a statement.
Nashville CEO Ian Ayre, formerly of Liverpool, said: "In what has been a challenging year, and in an uncharted environment created by the tornado that devastated our city and COVID-19, this is another big disappointing outcome for Nashville SC and its supporters."
FC Dallas have already been taken out of the tournament due to positive COVID-19 tests for 10 players and one coach, while other stars - including reigning MVP Carlos Vela - have opted against travelling to Florida.
The tournament, which will form part of a 2020 regular season that was suspended in March due to the pandemic, is going ahead despite the continued rise of confirmed cases in the United States, with the national tally surpassing three million.
MLS announced Chicago have been moved from Group A to Group B following Nashville's withdrawal and will face Seattle Sounders, San Jose Earthquakes and Vancouver Whitecaps.
Orlando City lead Group A after beating state rivals Inter Miami 2-1 in the tournament's first match on Wednesday, while Philadelphia Union picked up three points against New York City on Thursday.
LAFC claimed derby honours in Los Angeles thanks to second-half goals from Danny Musovski and star Carlos Vela on Sunday.
The Galaxy – without stuttering former Manchester United and Real Madrid forward Javier Hernandez – were dealt a blow in the 25th minute when centre-back Giancarlo Gonzalez was red carded after denying a goal-scoring opportunity.
Referee Kevin Stott had initially awarded a penalty and shown Gonzalez a yellow card before VAR intervened, with Diego Rossi brought down just outside the box as the Galaxy defender saw red.
LAFC had gone 238 minutes without scoring against the Galaxy – having averaged a goal every 28.6 minutes in the first seven derbies – but that drought ended courtesy of Musovski's 58th-minute opener at Banc of California Stadium, the forward getting on the end of Rossi's throughball.
Vela came off the bench with 20 minutes remaining for his first appearance since August 22 due to a medial collateral ligament (MCL) injury.
The reigning MVP capped his long-awaited comeback for the Supporters' Shield holders with a goal in the third minute of stoppage time, taking Vela to 23 goals from his previous 22 MLS matches at Banc of California Stadium.
With the result, LAFC are fourth in the Western Conference and five points adrift of leaders Sporting Kansas City, while the Galaxy remain rooted to the foot of the table.
Birthday boy Vela scored a stunning chip on the stroke of half-time to ensure reigning Supporters' Shield champions LAFC made the perfect start to the 2020 season on Sunday.
Co-owner David Beckham, his famous wife Victoria and Inter's hierarchy were in the stands as the expansion franchise made history in Los Angeles.
Inter battled in their first-ever MLS match but Diego Alonso's side came unstuck following a moment of brilliance from Vela on his 31st birthday.
Former Arsenal forward Vela – who scored a record-breaking 34 goals in a MVP season last term – chipped the ball over Inter captain and goalkeeper Luis Robles in the 44th minute at Banc of California Stadium.
"Surely we have to improve in football, but with this heart and with this intensity with which the team plays, we will surely win many games," said Inter head coach Alonso.
"Against maybe the best team in the league we gave a tremendous picture today of what we can become. With only six weeks of work, the merit is certainly from the footballers for what we have done today and the work they have done."
Seattle Sounders started their title defence with a dramatic 2-1 victory at home to Chicago Fire thanks to substitute Jordan Morris' brace.
Trailing to Robert Beric's 46th-minute opener, the Sounders equalised via Morris just past the hour mark before he netted the winner in the third minute of stoppage time.
Elsewhere, Kevin Molino scored twice as Minnesota United upstaged Portland Timbers 3-1, New York Red Bulls edged Cincinnati 3-2 and 10-man New York City lost 1-0 away to Columbus Crew.
The MLS All-Stars appeared to be cruising to victory before Kevin Alvarez's spectacular late strike was followed up a decent penalty shout for a Deandre Yedlin handball which was declined.
The hosts had won last year's edition 3-2 on penalties after a 1-1 draw and they seemed destined for another triumph when former Mexico international Vela headed home early.
Diego Palacios jinked his way to the left side of the edge of the box before delivering an inch-perfect second-minute cross for LAFC teammate Vela to nod in.
Minnesota goalkeeper Dayne St Clair, one of numerous first-half substitutes, maintained the MLS All-Stars' lead from a 43rd-minute Juan Dinenno header.
The hosts added a second in the 73rd minute when Jesus Ferreira found Carles Gil inside the box, with his control bobbling up but drawing a poorly timed tackle from Jesus Angulo, with referee Joe Dickerson pointing to the spot.
Seattle Sounders striker Raul Ruidiaz stepped up and sent Liga MX All-Stars goalkeeper Carlos Acevedo the wrong way.
The visitors pulled a goal back in the 85th minute when Pachuca's Alvarez drove in a thunderbolt from outside the box.
A minute later, German Berterame stooped to head a cross but was bundled over under pressure from Yedlin, whose arm was raised near the ball, but Dickerson waved away any penalty claims.
Carlos Vela scored a double, with both goals coming from the penalty spot, as LAFC secured only their second victory from their past eight games.
LAFC have a 15-1-0 record when scoring first this season although Houston leveled the game in the 24th minute from Corey Baird's classy goal after Vela netted an eighth-minute spotkick.
Vela restored LAFC's advantage from the spot on half-time after Fabrice Picault's handball was spotted by the VAR, with Ryan Hollingshead lifting home a third in the 52nd minute.
LAFC remain top of the Western Conference, nine points ahead of second-placed Austin, with two more matchdays until the postseason begins.
Gonzalo Higuain scored a 94th-minute winner to boost Inter Miami's playoffs hopes with a 3-2 road win over DC United, who had Christian Benteke net his first goal for the club.
Higuain struck the winner in the fourth of eight stoppage-time minutes, with a first-time strike from Deandre Yedlin's low cross from the right.
Benteke had opened the scoring in the 22nd minute with a back-post left-foot volley, before Leonard Campana's double for Inter.
Taxiarchis Fountas equalised in the 57th minute before Higuain's late winner, which means Inter are seventh in the Eastern Conference, moving above Columbus Crew, who conceded again late in a 1-1 draw with Portland Timbers on Sunday.
The Crew were denied all three points with Santiago Moreno lashing home a 95th-minute equaliser for the Timbers, after Kevin Molino's first-half strike.
Vela struck twice within six first-half minutes, first from the penalty spot before getting in behind the Colorado defence and calmly finishing past goalkeeper William Yarbrough.
The former Mexico international produced his best goal of the game to complete his hat-trick in the 50th minute, curling in a fine left-footed shot from just inside the box.
Vela only managed five goals from 20 MLS appearances last season with LAFC head coach Steve Cherundolo cautiously optimistic about his potential impact this term.
“We will have to wait and see what it does. But I think we all know what he can do,” Cherundolo said. “He showed it again today and he worked very hard in preseason to get to where he is today. I'm very happy for him and the group that we're all rewarded for it.”
Yimmi Chara's spectacular 78th-minute goal earned Portland Timbers a 2-2 draw with 2021 Supporters' Shield winners New England Revolution.
Portland, who reached the MLS Cup final last year, found a way back with Chara firing home a stunning overhead goal while Jozy Altidore debuted for the Revs as a 79th-minute substitute.
Ex-Liverpool and Bayern Munich midfielder Xherdan Shaqiri made his debut for Chicago Fire as they drew a blank in a 0-0 draw at Inter Miami.
Leonardo Campana's 10th-minute header from Gonzalo Higuain's cross hit the crossbar for Miami, while Chicago's Stanislav Ivanov struck the upright in the 31st minute. Shaqiri was impressive throughout, with a long-range first-half chance his only major goal attempt.
Toronto, who made a major off-season signing with Lorenzo Insigne to join in July, only managed a 1-1 draw at Dallas.
Philadelphia Union started its new season with a 1-1 home draw against Minnesota United, with Cory Burke levelling Robin Lod's 23rd-minute strike.
New York Red Bulls won 3-1 at San Jose Earthquakes, while Columbus Crew swept aside 10-man Vancouver Whitecaps 4-0.
Cecilio Dominguez netted a double as Austin won 5-0 over last year's bottom side Cincinnati, while Michael Estrada scored a brace as DC United eased past newcomers Charlotte 3-0.
