The 28-year-old attacking midfielder suffered an ankle injury during the Premier League game against Everton at the Boleyn Ground on Saturday afternoon.
The France international, who joined the Hammers from Ligue 1 outfit Marseille in the summer transfer window, picked up the injury to his left ankle after a challenge from midfielder James McCarthy.
Payet tried to shake it off but he had to be substituted in the 50th minute, as the game in London ended in a 1-1 draw.
The former England international, though, believes that Hammers’ fans should remain optimistic because of a good squad.
Payet has been one of the best players in the Premier League so far this season, and has scored five goals and created 46 chances in 12 league matches.
The former Lille attacker has a pass accuracy of 82% and a shot accuracy of 65%, and has won one header, 28 dribbles and seven tackles.
West Ham are sixth in the Premier League table at the moment with 21 points from 12 games, just three points behind fourth-place Manchester United.