The injury-prone centre-forward has an adductor problem sustained in the weekend's 2-2 draw with Norwich City and will not make the trip to Ewood Park for the fifth round fixture on Sunday.
Carroll has made 18 appearances for the Hammer this season having been restricted due to ankle, foot, thigh and hamstring injuries. He spent seven months on the sidelines last year after undergoing surgery on damaged knee ligaments in February.
Fellow attacker Enner Valencia will also miss after being forced off at Carrow Road with an ankle issue.
In some more positive news for the East London club, Argentine playmaker Manuel Lanzini is expected to play some part against Rovers after missing the past six weeks with a thigh injury.