The Senegal international sustained the injury during the second half of the 3-1 victory at Upton Park on Saturday, but stayed on to complete the 90 minutes after receiving treatment.
On Monday, West Ham's co-owner David Gold announced the news via his official Twitter account, with Kouyate set to be out until November.
"Bad news. C.Kouyate will be out for 6 weeks," he posted.
"He will probably miss 5 games and might be available for Aston Villa at home 8 nov [November]. dg.
"In the past losing a player like C.Kouyate would be devastating but now we have quality back up. Cheikhoe [sic] get well soon. dg."
Sam Allardyce's side travel to Manchester United on Saturday.
'I’d probably pick Cole Palmer alongside Bellingham and Rice in there at the moment. For me, Declan Rice is good enough to play that central midfield role on his own' Thomas Tuchel advised to DROP Manchester City star by England legend
Manchester United staff threatened with sacking for leaked information... in a leaked email
