"The Yorkshire all-rounder had surgery on his left shoulder on Friday to further assess the injury he sustained while bowling in the third ODI against India last month," the England and Wales Cricket Board said in a statement.
He has suffered a partial tear of a tendon and will be out of action until April, the board said.
He will be replaced by Steven Finn.
England will fly to the Caribbean next Wednesday.
England will play two warm-up matches and three ODIs against the West Indies in the upcoming days.
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