Lampard was forced off during Chelsea's Champions League defeat to Shakhtar Donetsk on Tuesday night with a recurrence of the injury that saw him miss England's World Cup qualifiers against San Marino and Poland.
Manager Roberto Di Matteo confirmed in his weekly press conference that Lampard will be missing for a fortnight with the problem.
"He is going to be out for a few weeks," Di Matteo said. "He's got a calf problem, so we will miss him and it's a big loss for us. Apart from him everybody else is fit. Marko Marin might be in the squad for Sunday."
Lampard will be unavailable for Sunday's game, the Capital One Cup clash against United on October 31, the trip to Swansea in the Premier League next weekend and Shakhtar's visit to London on November 7.
However, he will be hoping to return to action for the home game against Liverpool on November 11.
Lampard has been on the bench a number of times this season with Ramires and John Obi Mikel providing strong competition for places at the base of the midfield.