The Colombian finished sixth in this year's competition, which was won by Danish rider Jonas Vingegaard.
However, the UCI announced on Wednesday that two samples of Quintana's blood showed traces of tramadol, a banned substance.
The 32-year-old has 10 days to appeal the ruling with the Court of Arbitration for Sport (CAS), though he has not been banned from competition as it is a first offence.
Quintana's sixth place in the General Classification was his first top-10 Grand Tour finish since the 2019 Vuelta a Espana, and his best performance in the Tour de France since 2016.
The Arkea-Samsic team announced that Quintana had signed a contract extension until 2025 on Tuesday, though he was not named in their squad for this year's Vuelta a Espana, which starts on Friday.
The team released a statement on Wednesday saying: "The Arkea-Samsic team took note of the notification from the UCI and received by Nairo Quintana informing him of the presence of tramadol in two samples of dried blood collected during the last Tour de France.
"Since March 1, 2019, the UCI medical regulations have provided for the banning of tramadol in competition for medical reasons.
"Furthermore, this violation of the UCI medical regulations does not lead to a suspension for the rider.
"The Arkea-Samsic team will not provide any further comment."
Arkea-Samsic rider Quintana launched a late attack in the closing four kilometres, crossing the line 47 seconds ahead of Tiesj Benoot.
It means Quintana – who crashed in stage two – finished sixth in the general classification, with Max Schachmann having maintained his overnight lead to claim the overall triumph.
With Sunday's stage cancelled due to the spread of coronavirus, French rider Romain Bardet criticised race organisers, claiming he could not understand why Saturday's event was going ahead.
After the race's completion, Quintana also referenced his concerns over the ongoing pandemic, acknowledging his main focus was now on being with his family.
"Now we'll try to return to Colombia, spend time with the family while this important problem for the world is resolved," the 30-year-old told reporters.
"We are aware of what is happening, we've finally finished and we will also be quarantined so that this virus does not continue to spread.
"We have to listen to the authorities so that this does not get out of hand and we can all return to work soon."
Despite a difficult start to the event, Quintana was thrilled to have finished on a high with a third stage win of the season.
"I always try to win like this, with elegance and a good attitude," he added. "We were highly motivated to do things well and have been working hard.
"The team worked hard to catch the break and then I did what I had to do. There was nothing I could do for the GC, so I knew I had to attack today, because I wanted to bring joy to the team, because of the effort that everyone has made. It is a gift for all of them. I always demand a lot, but here are the results."
While the stage belonged to Quintana, it was Schachmann who claimed the general classification victory.
Team Sunweb's Benoot started the day 36 seconds behind Schachmann, who also had to deal with challenges from Vincenzo Nibali, Thibaut Pinot and Sergio Higuita.
With Quintana already far up ahead, Benoot rolled the dice with just over 1,000m to go, and although he established a gap, Schachmann piggie-backed onto Higuita's chase to ensure an 18-second winning margin.
"It was a really hard finish, in the last three kilometres I worked through hell and a world of pain," Schachmann said.
"But now it's like being in heaven. Every little bit of pain in my legs was worth it. This is one of the biggest wins of my career and one of the most important steps."
The Colombian is a two-time runner-up at the Tour, most recently in 2015, and has won both the Giro d'Italia and the Vuelta a Espana.
Quintana moved to the France-based Arkea-Samsic team from Movistar ahead of the new season, having spent eight years with his previous employers.
The 29-year-old's new team includes Frenchman Warren Barguil, who won the mountain classification at the 2017 Tour, and three-time points classification runner-up Andre Greipel.
This year's edition begins in Nice on June 27, concluding with the processional final stage in Paris on July 19, with Team INEOS' Egan Bernal out to defend his title.
On Wednesday, Quintana was retrospectively disqualified from this year's Tour de France for an in-competition drug infringement.
The Colombian finished sixth in the General Classification, his first top-10 Grand Tour finish since the 2019 Vuelta and his best performance in the Tour de France since 2016.
However, the UCI announced that two samples of Quintana's blood showed traces of tramadol, a banned substance.
The 32-year-old was given 10 days to appeal the ruling with the Court of Arbitration for Sport (CAS), though he has not been banned from competition as it is a first offence.
On Thursday, the Colombian confirmed he would not be riding in the Vuelta, despite initially stating he would be doing so.
In a widely reported statement, Arkea-Samsic rider Quintana said: "I communicate that I will not participate in the Vuelta to assert my reasons before the Court of Arbitration for Sport, I will return to the calendar races at the end of the season."
Quintana had responded to the allegations via his social media channels, stating: "I have been surprised by the announcement of the UCI of an infraction for use of tramadol.
"I am completely unaware of the use of this substance and I deny having used it in my career.
"With my team of lawyers we are exhausting all the processes to assume my defence.
"I also want to ratify that I will be in the Vuelta a Espana, riding my best for the team, my country and my fans."
