Carroll, on a season-long loan from Liverpool, was left out of Saturday's Barclays Premier League game with Chelsea because of the injury he suffered in the midweek loss to Manchester United. Carroll was replaced by Carlton Cole after 62 minutes of that game and Cole came into the starting line-up to play Chelsea.
Allardyce told BBC Sport: "It's pretty severe. We didn't expect it to be quite as severe. It's going to be about six to eight weeks. It's a blow for us and Andy."
Having already missed a month due to a hamstring injury suffered against Fulham in September, Carroll had netted only once in 10 games for the Hammers.