After scoring the only goal of the game at Old Trafford, the South American eventually had to be replaced after failing to shrug off a hefty first-half bang on the ankle.
Tevez was carried into the tunnel by two members of the United's backroom staff after the final whistle, with manager Sir Alex Ferguson confirming it is unlikely he will be involved at Villa Park next week.
"It was a bad tackle and the longer the game went on, the worse the injury got," said Ferguson.
"In the end, we had to bring Carlos off. We will assess him tomorrow to see what the damage is but he is doubtful for Saturday now."
Ferguson should have a ready-made replacement for Tevez in Wayne Rooney, who missed a second successive game with a virus but is showing signs of being fine for the weekend.
The Scot explained: "It would have been a bit of a risk to play Wayne today but he should be fine for Saturday."
Ferguson was less than impressed by his team's efforts, describing United's performance as 'careless'.
Certainly, Tevez's goal - with the striker finding Cristiano Ronaldo with an overhead kick before racing on to an inspired back-heeled return pass - was at odds with the rest of a mundane contest.
Tevez also hit the post on two occasions, although even this failed to lift a crowd which was almost silent on occasion, drawing a stinging rebuke from Ferguson.
"The crowd were dead," he remarked. "It was like a funeral out there.
"It was the quietest I have heard here for some time and the atmosphere today did not help us.
"There have been periods like that in the past. Some years ago, when we were dominant, the crowd came to be entertained.
"Sometimes we need them to get behind us. They can help produce the right performance but we did not get that today."
Instead, the flat atmosphere only induced more sloppiness from United ranks, which would have proved costly if Mikael Forssell had found the target with two late chances.
"It only takes a second to score and we made it difficult for ourselves. it was a careless performance," added the United boss. "Our finishing was shoddy and by being as careless as as we did, we could have been embarrassed."
Ferguson admitted Tevez's strike was the one bright spot on an otherwise disappointing day, although his team do remain two points adrift of leaders Arsenal.
"It marvellous goal and I think Carlos will go on to get 20 now," said the Scot, who celebrated his 66th birthday yesterday.
"Once we are over the New Year period, we can have a look at where we are. But effectively, the season starts now and it could be nip and tuck right to the end."