The 24-year-old was forced off just before the interval during Sunday's 2-1 victory over Leicester City at Villa Park.
Westwood sustained the injury after a late challenge from Leicester's Jamie Vardy, for which the forward was given a yellow card.
Having been replaced by Kieran Richardson, Westwood has now been ruled out by the club for between three and four weeks.
Westwood has started every Premier League game but one for Villa this season, having been a regular for the club since signing from Crewe Alexandra in 2012.
The injury comes as a further blow to Paul Lambert's midfield ranks, with Tom Cleverley a doubt for Saturday's derby clash against West Brom with a foot problem.
Fabian Delph is a long-term absentee with a shoulder injury.
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