Carroll, on a season-long loan from Liverpool who he joined for £35 millionin 2011, twisted his knee in the 1-0 defeat to Manchester United on Wednesday.
"Andy Carroll's injury is pretty severe. We didn't expect it to be quite as severe," Hammers boss Sam Allardyce told Sky Sports after revealing Carroll would play no part in the club's match against Chelsea at Upton Park on Saturday.
"It's going to be about six to eight weeks. It's a blow for us and Andy. We must soldier on. The lads out there have plenty of experience but we are a bit light on the bench."
Carroll, deemed surplus to requirements by Liverpool manager Brendan Rodgers in the close-season, has struggled for form and fitness since moving to the east London club.
The England international has scored only one goal in 12 Premier League appearances and was ruled out for a month with a hamstring injury earlier in the season.