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.
Local media reported on Wednesday that 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.
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.
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