Lampard's injury is yet another setback for Chelsea's title aspirations as they trail Premier League leaders Manchester United by seven points.
Manager Avram Grant is already without captain John Terry and striker Didier Drogba through injuries.
Ricardo Carvalho faces a likely three-match suspension after he was sent off for a two-footed tackle on Gabriel Agbonlahor at Stamford Bridge.
Chelsea have confirmed they will not appeal against Carvalho's dismissal, but will do so for Ashley Cole, who was also sent off for deliberate hand ball in stoppage time against Villa.
The England left-back will have his case heard by the Football Association on Friday.
"It was not easy before without the injured and it's still not easy now, but this is the situation and we need to make the best of it," Grant told BBC Radio Five Live.
Grant's problems will be further exacerbated when he loses Drogba, Salomon Kalou, John Mikel Obi and Michael Essien to the African Cup of Nations in Ghana next month.
Their departures, along with injuries and suspensions, will mean the Israeli is likely to dip into the transfer market to strengthen his weakened squad.
"Everything is always about January because the transfer window is open," said Grant.
"The injured players and the African Nations Cup will make us think more about what we need to do."
Lampard had been sidelined by a thigh injury for six weeks earlier in the season.
The 29-year-old is Chelsea's joint top scorer, along with Drogba, with nine goals in all competitions this season.