The powerful 24-year-old Senegal international was injured towards the end of his side's impressive 3-1 home win against last season's league runners-up on Saturday but was forced to stay on the pitch because manager Sam Allardyce had used all three of his substitutes.
British media reports said Kouyate underwent scans on Monday to determine the extent of a groin injury.
"Bad news. C.Kouyate will be out for 6 weeks. He will probably miss 5 games and might be available for Aston Villa at home 8 Nov," Gold said on his official Twitter account.
The club was yet to confirm the injury.
Kouyate moved to the club from Anderlect for a reported seven million pounds in July and has so far impressed in his five league outings with a series of dynamic performances from the centre of midfield.
West Ham are eighth in the league and visit Manchester United on Saturday.
(Reporting By Sam Holden)
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