"It's not broken, but if I continue to play it will be broken in a few days," said an emotional Nadal, the fourth seed.
"This is a very bad position, but that's life. If this was not Roland Garros I probably would not have taken the risk of playing in the first couple of days."
Nadal, a 14-time Grand Slam title winner, has been plagued by injuries throughout his career, affecting his knees and wrist.
French Open: Nadal wins 200th Grand Slam match
A right wrist injury forced him to skip the 2014 US Open.
Despite his latest setback, the charismatic Spaniard said he will keep playing although his participation at Wimbledon next month is now in serious doubt.
"Nine times in my career I have been able to be healthy here in Paris and win this tournament," he said.
"This is a tough moment and the toughest press conference I have ever had to give but it's not the end."
Nadal had coasted through the first two rounds in Paris dropping just nine games but revealed he had needed pain-killing injections in his wrist to take part.
Flawless Nadal races into French Open second round
His withdrawal gives compatriot Marcel Granollers a walkover into the last 16.
It's also a huge boost to Novak Djokovic's hopes of lifting a first French Open crown.
Nadal and Djokovic were due to meet in the semi-finals next Friday -- the date of the Spaniard's 30th birthday.
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