"I don't think he'll play against Spain and if it's very bad he won't play against Russia either."
The injury appears to be worse than first feared, however, and even if Sweden progress to the quarter-finals Wilhelmsson, who has scored 14 goals in 50 internationals, will miss out.
The Nantes midfielder's injury took the gloss off Sweden's 2-0 win, which was secured through goals from Zlatan Ibrahimovic and Petter Hansson.
Aside from Wilhelmsson, who cannot be replaced, midfielder Niclas Alexandersson is a doubt for Sweden's next match against Spain in Salzburg on Saturday.
Lagerback's side then play Russia in Innsbruck on 18 June.
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