The Liverpool forward moved to Upton Park in the summer on a season-long deal but suffered the injury in the midweek defeat at Manchester United.
Carroll, who missed several weeks earlier in the campaign with a hamstring problem, was substituted shortly after the hour mark at Old Trafford and further assessment has now identified the £35million man will be ruled out for the remainder of 2012.
West Ham boss Sam Allardyce fears the England international, who only scored his first goal of the season in last weekend's defeat at Tottenham Hotspur, may not return until February.
"It is pretty severe - lateral ligament, I think," Allardyce told Sky Sports ahead of Saturday lunchtime's Premier League kick-off against Chelsea.
"We did not expect it to be quite as severe as it was but it looks like maybe six to eight weeks. So that is a bit of a blow for us and Andy.
"But we must solider on. There is not a lot we can do about these trauma injuries."