Carroll has had a series of injury setbacks since joining West Ham from Liverpool in 2012, initially on a season’s loan before the deal was made permanent.
The forward, who has played nine times for England, has spent about half of his time at the club out injured.
His latest setback adds to a growing casualty list for Bilic.
Aaron Cresswell, Sofiane Feghouli and Manuel Lanzini are also out injured, while midfielder Dimitri Payet is still regaining full fitness, having been given a break after helping France reach the final at Euro 2016 in July.
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