Stokes, 22, sustained the injury when he lashed out in frustration in the changing room after being dismissed for a golden duck against the West Indies recently in the third Twenty20 international in Bridgetown.
The injury ruled him out of the World Twenty20 in Bangladesh and also makes him a doubt for the start of England's domestic summer programme.
"England and Durham all-rounder Ben Stokes has had an operation on the fractured scaphoid bone in his right wrist," the ECB announced in a statement.
"Stokes will be reviewed in six weeks and a schedule for his return to full training will be determined following the review."
England's first domestic fixture against Scotland takes place on May 9, which is seven weeks away, with a one-day series against Sri Lanka starting on May 20.
Ben Stokes undergoes surgery on self-inflicted wrist injury
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