The 22-year-old was ruled out of England's World Twenty20 campaign in Bangladesh because of the injury, which occurred when he punched a dressing room locker following a dismissal against West Indies in Barbados earlier this month.
New Zealand-born Stokes had the operation to repair the fractured scaphoid bone in his right wrist, the ECB said in a statement, and his progress would be reviewed in six weeks to determine when he could resume training.
Stokes was one of the few England players to emerge with credit from their poor tour of Australia, in which they lost the Ashes test series 5-0 and won only one international game on tour, and his injury was a blow to their Twenty20 hopes.
England face New Zealand in their opening World Twenty20 clash in Chittagong later on Saturday.
After the Bangladesh tournament, England play a one-day international against 2015 World Cup qualifiers Scotland on May 9 in Aberdeen before hosting Sri Lanka in May and June.