The striker suffered the setback in Wednesday's 0-0 Premier League draw at Southampton, but remained on the pitch as the visitors had used all three substitutions.
Allardyce, who saw goalkeeper Adrian dismissed in that match, provided an update on Carroll's prognosis ahead of Saturday's FA Cup tie at West Brom.
"A full diagnosis on Andy is yet to come and we should have that today, but it looks like a few weeks," Allardyce said on Friday.
"The medial ligament on the inside of his knee has a little tear from a fairly innocuous collision with the defender.
"If we're lucky it could be four to six weeks. It's a big blow for him and us but one we've got to cope with."
Adrian was sent off just past the hour mark at St Mary's Stadium after attempting to wrong-foot the oncoming Sadio Mane, only to lose control and handle the ball outside the area.
Allardyce felt his goalkeeper had been fouled and questioned the justification of the red card, having already declared his intention to appeal.
"I think that looking at Adrian's red card it's not just the foul on him, but was it a goalscoring opportunity?" he said.
"You get sent off if it's denying a goalscoring opportunity and if you look at the situation we don't think it was denying one."
Victory this weekend would send West Ham into the quarter-finals of the FA Cup and that is Allardyce's sole focus at The Hawthorns.
"Our run in the FA Cup up to now has been very good, it's given us a lot of joy," he added.
"The West Brom game is about winning, so we have to go there and try to win."
