Carroll, who cost Liverpool a club-record £35 million pounds last year but was frozen by new Reds boss Brendan Rodgers, joined the Hammers on a season-long loan last week.
He fell awkwardly midway through the second half of his debut match as West Ham beat Fulham, and was ruled out of England's World Cup qualifiers against Moldova and Ukraine this month.
Scans have now revealed the hamstring injury is worse than expected and that the 23-year-old will be out of action for up to a month-and-a-half.
West Ham have confirmed the severity of the injury, with co-owner David Gold writing on Twitter that a six-week absence is the "worst case scenario."
Liverpool boss Rodgers has been left missing firepower up front after failing to secure a top-notch striker before the transfer window closed on Friday, and said earlier this week he would not have allowed Carroll to leave on loan had he known he would be unable to strengthen his squad.
- West Ham
- Brendan Rodgers