The British number one, 20, has struggled with the problem in recent months and had been expected to have an operation at some point.
However, the former world number 27, now ranked in the 60s, has decided to have the procedure immediately, with a view to returning in time for the US Open swing.
"I wanted to inform my lovely supporters that I have decided to have minor wrist surgery at the Mayo clinic with one of the best wrist doctors in the world, Dr. Richard Berger," Robson said on her Facebook page.
"Dr. Berger is very confident that I will be able to return to the tennis court pain free before you even have time to miss me.
"Although sadly, I will have to miss the French Open and Wimbledon."
The decision appears to be a calculated one - Robson tends to struggle on clay, and her best performances have come at Flushing Meadows, where she reached the fourth round in 2012 and the third stage last season.
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