Chapple was returning to his club, Lancashire, for treatment and would be replaced by Worcestershire's Kabir Ali, the England and Wales Cricket Board (ECB) said in a statement.
Chapple suffered the injury during England's win over Ireland on Tuesday when he made his one-day international debut.
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"Obviously it's very disappointing for Glen but everyone hopes that after receiving the right treatment at Lancashire he'll be able to rejoin the squad and play a part in the latter stages," England's chairman of selectors, David Graveney, said.