The Senegal international was forced off in the second half of the 1-1 Premier League draw at Manchester United on Monday (AEDT) and was sent for tests in London.
The club has now announced that the 26-year-old, who scored inside two minutes at Old Trafford, is not likely to return until the new year.
"Diafra Sakho will be out for six weeks after sustaining a thigh injury during Sunday's draw with Manchester United," the club confirmed.
"A scan on Tuesday revealed that the injury will keep him out of contention for up to six weeks.
"Everyone at West Ham United wishes him a speedy recovery and quick return to action."