The news comes as a major blow to caretaker boss Eddie Gray, with the Marseille man having been one of the better performers during this season, of all season's.
Sakho joins centre-back Roque Junior on the sidelines, the Brazilian suffering an achilles injury while on international duty last week.
Leeds did received a boost, though, with Gary Kelly and Dominic Matteo expected to be back for this weekend's trip to Charlton, along with Alan Smith.