Sakho, who has scored 10 goals in his debut Premier League season, limped off with a thigh injury just before the hour mark against Stoke, a game the Hammers drew 1-1 after conceding a goal to Marko Arnautovic deep into added time.
He will have a scan on the problem on Monday, while Enner Valencia is also being monitored after he came off 12 minutes from time with a foot injury.
Allardyce said: “Enner was never going to be able to play the full 90 minutes, but he got a kick as well and we’re hoping it won’t be enough to keep him out for next week, because Diafra will definitely be missing.
“If it’s a thigh strain, depending on what grade it is, it could be two weeks or it could be him missing the rest of this season, but we will wait and see.
“That leaves us very short on the front line with Andy (Carroll) being out, and means goals will be fewer and farther between than they used to be, so if we don’t get that defensive side right then the last six games are going to be tough for us.”