The 26-year-old played only 35 minutes of his league debut for the east London club before he had to be taken off.
The club confirmed a scan on Wednesday showed the new signing from Swansea had “a significant injury”.
They added it was too early to put a timeframe on a potential return date for the Ghana forward.
Stijn Vandenbroucke, the head of West Ham’s medical and sports science team, said it was “imperative that we do not rush to conclusions and we receive the correct diagnosis by consulting top specialists”.
He added: “My first thought and priority is with the player and his physical and mental wellbeing.
“The best thing we can do as a club is to support Andre through this difficult period.”