The Chilean opened the scoring at The Hawthorns, but then fell awkwardly and twisted his left knee and had to be replaced by Niko Kranjcar.
QPR revealed earlier on Monday that they were awaiting news on the extent of the damage, before later confirming that Vargas sustained a grade two medial collateral injury.
He is expected to be out for 10-12 weeks, and the news represents a big blow for Chris Ramsey's side, who remain three points from safety with seven matches remaining.
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