The 22-year-old Durham player punched a locker after being dismissed for a duck against West Indies earlier this month, forcing him to withdraw from his first global tournament.
While his team-mates carried on from the Caribbean to Bangladesh, he went home for treatment and is due to be assessed in six weeks, when he should find out when he can return to action.
With England's first fixture against Scotland on May 9, time looks tight for Stokes to be in contention.
The one-day series against Sri Lanka, beginning 11 days later looks a more likely comeback date, should his recovery go to plan.
An England and Wales Cricket Board statement said: "England and Durham all-rounder Ben Stokes has had an operation on the fractured scaphoid bone in his right wrist.
Stokes will be reviewed in six weeks and a schedule for his return to full training will be determined following the review."
- Sports & Recreation