The 22-year-old defender was substituted in the 81st minute of Wednesday's match at the Allianz Arena, which Bayern won courtesy of goals from Franck Ribery and Mario Gotze to reach the last 16.
After the game, Bayern confirmed via their official Twitter account: "David Alaba picked up a medial collateral ligament injury in the match. There will be further tests in the morning."
Coach Pep Guardiola added: "We must adapt to the situation. We hope he comes back quickly."
Bayern's victory on Wednesday ensured their place in the knockout stages as winners of Group E.
The German champions, who have a 100 per cent win record from their four games in this season's competition, dominated Wednesday's game, producing 24 attempts on goal to Roma's five.
It was a tighter game than the one between these two teams in Italy two weeks ago, which finished 7-1 to the Germans.
"I'd like to congratulate my players. I never expected to qualify and win the group after four matches," said Guardiola.
"The 7-1 was more of a coincidence, something like this happens once in a lifetime.
"Roma didn't want to suffer again so they played very defensive, with six defenders. Nevertheless we were dominant, especially in the second half."
Gotze, who took his tally of goals in 2014-15 to seven with his team's second on Wednesday, paid tribute to Guardiola, who is currently in his second season at Bayern.
"It's fun to play in this team. We won 2-0 and are very happy with this," said the World Cup winner.
"We knew that it would take some time to understand our coach but now we know how to fulfil his wishes."
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