The 26-year-old was forced off in Wednesday's 0-0 draw at Southampton as the Hammers finished the game with only nine men following a red card for goalkeeper Adrian.
Having missed the start of the season and much of last year with injuries it is yet another setback for Carroll, although Allarydce is yet to know the full extent of the latest issues.
"I think a full diagnosis is yet to come, it will probably be by the end of the day," he said.
"It is likely to be a few weeks, the medial ligament on the side of his knee has a tear in it from a fairly innocuous collision.
"Hopefully (he will only miss) four to six weeks if we are lucky, depending on Andy's recovery rate
It is a big blow for his and a big blow for us but it is one we have to cope with.
"It is traumatic when someone is going through a period when in a short time they overcome one injury and another occurs."
Source : PA
Source: PA