“I’m thinking about winning the tournament and for that I have to play five more matches. The doctor says that is 100 per cent impossible.
“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.
“It’s not broken, but if I continue to play it will be broken in a few days. This is a very bad position, but that’s life,” added Nadal, who showed no signs of the injury during his 6-3 6-0 6-3 second round win over Facundo Bagnis on Thursday, nor his first round hammering of Sam Groth in which he lost just three games.
“If this was not Roland Garros I probably wouldn’t take the risk of playing in the first couple of days,” he said.
This is the latest setback the 29-year-old Spaniard has suffered in an injury-plagued career.
Tendinitis in his knees prevented him from defending his Wimbledon title in 2009, while the 2008 Beijing Olympics gold medallist also missed the 2012 London Games because of injury.
After looking down and out in 2015 when he lost his French Open title and slumped to his lowest ranking in a decade, he had appeared reborn this season.
He captured the Monte Carlo and Barcelona titles to equal Guillermo Vilas’s record of 49 claycourt titles.
Despite the new injury Nadal is hoping he will be fit to play at Wimbledon next month.
“We’re going to work hard to be ready for Wimbledon,” he said. “I need a couple of weeks (with the wrist) immobilised. Then we’re going to do the treatment and we hope that works well.
“We expect to recover quick and to be ready for Wimbledon.”
His withdrawal hands compatriot Marcel Granollers a walkover into the last 16. It is also a huge boost to Novak Djokovic’s hopes of lifting a first French Open crown.
Nadal and top seed Djokovic were due to meet in the semi-finals next Friday.