The Sun is reporting that the Nigeria international is set for a significant spell on the sidelines after having suffered the problem during the first half of the 2-1 loss at Selhurst Park on Saturday.
The same report claims that Moses could be out of action for as long as six weeks in what is a fresh injury setback for the west London club.
Chelsea have already lost N’Golo Kante and Alvaro Morata to similar injuries in recent weeks, although it is thought that Morata will be fit to feature when the Blues take on Roma in the Champions League on Wednesday night at Stamford Bridge.
It has been a disappointing few weeks for Chelsea, with the Blues having suffered back to back Premier League defeats to leave them fifth in the table and nine points behind leaders Manchester City after eight games of the new campaign.
Chelsea will aim to get back to winning ways in the Premier League when they take on Watford next weekend.
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