Jackson told NFL Network's James Palmer he tested positive on Wednesday after having flu-like symptoms, chills and being congested.
The 32-year-old becomes the second known NFL player this week to be diagnosed after Dallas Cowboys running back Ezekiel Elliott on Monday.
Broncos star pass rusher Von Miller announced in mid-April he contracted coronavirus to become the second NFL player to publicly announce a positive test following Los Angeles Rams center Brian Allen.
It is unknown when Jackson contracted the virus, but he did participate in a march in Denver earlier this month to protest racial inequality in the wake of the death of George Floyd.
A first-round pick out of Alabama in 2010 by the Houston Texans, Jackson spent his first nine seasons in Houston before joining Denver in 2019.
He was fourth on the Broncos in tackles last season with 71 and had two interceptions to give him 18 in his career.
The Broncos were humbled 31-3 by the Saints in the absence of starting quarterback Drew Lock and backups Brett Rypien and Blake Bortles on Sunday after the trio were deemed closed contacts of signal-caller Jeff Driskel, who was placed on the reserve/COVID-19 list.
Makeshift quarterback Kendall Hinton completed just one of nine passes for 13 yards and two interceptions.
Denver became the first team with one or fewer completions and fewer than 20 passing yards in a game since the San Diego Charges in 1998 – Ryan Leaf completed one of 15 passes for four yards in that game.
"I was disappointed on several levels, that our QBs put us in that position, that our QBs put the league in that position," Fangio said.
"We count on them to be the leaders of our team, the leaders of our offense, and those guys made a mistake."
Fangio added: "They got lax with their masks, I guess, and they got lax with their distancing, I guess.
"I haven't done a good enough job of selling the protocols to them when they're on their own. That's on me."
Undrafted rookie wide receiver Hinton came off the practice squad, had zero practice reps and competed in his first NFL game as the Broncos' quarterback in an unprecedented situation.
"When I got the call, it was pure excitement. Of course, there was nerves and disbelief,'' Hinton said. "Coming in, I knew I had no idea of what the speed of the game was like.... We knew it would be a tough situation, for sure.''
Broncos safety Kareem Jackson said: "I feel like maybe [the game] could have been moved, but at the same time, maybe the league was making an example of us as far as maybe not doing the things we needed to do in that particular room, that quarterback room.
"Obviously, the guys didn't follow their protocols, and for [the NFL] to see that, I guess they felt like they had to make an example, so at the end of [the] day, it is what it is.
"... Obviously, it's our guys' fault for not wearing their masks, but at least maybe move the game to the next day or whenever so we're given a fighting chance,'' Jackson added. "[It's] obviously disappointing. I'm not sure why it wasn't moved. I have no clue... as a competitor, [it is] definitely frustrating.''
