The 27-year-old suffered a knee injury during the Europa League play-off against Astra Giurgiu on Thursday.
The club have yet to put an official time frame on his recovery but estimate he will be out of action for four to six weeks.
The news comes as another blow to Carroll, who has spent around half of his four-year spell with the Hammers out injured.
His latest setback also adds to a growing casualty list for manager Slaven Bilic, who this week lost club-record signing Andre Ayew for four months to a thigh injury.