Tramadol was banned by the UCI in 2019 although infringements of the in-competition ban are offences under medical rules and do not constitute an anti-doping violation.
Quintana finished sixth overall in this year's Tour but will now have his results deleted. However, he will not face a ban and is free to ride in the Vuelta a Espana, which starts in Utrecht on Friday.
A statement said: "The Union Cycliste Internationale (UCI) announces that the Colombian rider Nairo Alexander Quintana Rojas has been sanctioned for an infringement of the in-competition ban on using tramadol as set out in the UCI Medical Rules with the aim of protecting the safety and health of riders in light of the side-effects of this substance…
"As this is a first offence, Nairo Alexander Quintana Rojas is not declared ineligible and can therefore participate in competitions."
Quintana, 32, had two top-five finishes for Arkea-Samsic on stages during this summer's Tour, with his best a second place behind overall winner Jonas Vingegaard on stage 11 on the Col du Granon.
That stage took place on July 13, one of two days during the Tour when Quintana provided blood samples which later revealed traces of tramadol.
The other was on July 8, a day after Quintana finished fifth on stage six into Longwy.
Quintana has 10 days in which he can lodge an appeal against his disqualification with the Court of Arbitration for Sport.