Savic was shown a straight red card after an incident involving Chelsea's Antonio Rudiger in the second leg of the Champions League last-16 tie at Stamford Bridge on March 17.
The Montenegro international has been disciplined by UEFA for "assaulting another player", as well as "directing abusive language at a match official".
Diego Simeone also received a warning over a late kick-off to the fixture, while the club itself received a €10,000 fine. Atleti were also ordered to pay a further €14,000 for "improper conduct of the team".
Atletico lost 2-0 on English soil – Hakim Ziyech and Emerson Palmieri scoring the goals – as the LaLiga side exited the competition 3-0 on aggregate.
Savic started all eight of his team's Champions League outings in 2020-21, with the dismissal against the Blues his third in the competition.