Manager Roberto Di Matteo confirmed the injury on Friday.
Lampard won't be available for Chelsea's significant matches at home against Manchester United in the English Premier League and League Cup, as well as the visit of Shakhtar Donetsk in the Champions League.
The England international limped off the pitch after just 15 minutes in the midweek 2-1 loss at Shakhtar Donetsk. The match was Lampard's 100th in the Champions League.
The same injury kept him out of England's two World Cup qualifiers this month, and may influence his selection in Roy Hodgson's next squad for a friendly against Sweden on Nov. 14.