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Having been replaced by Kieran Richardson, Westwood has now been ruled out by the club for between three and four weeks.
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.
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