He announced his withdrawal the day before he would have been scheduled to play in the third round.
The left-handed Spaniard wore a blue brace on his wrist during what he called "one of the toughest press conferences in my career."
Nadal, who owns a total of 14 Grand Slam titles, said he would not even have tried to compete at any other tournament with the injury, "but it's the most important event of the year for me."
He won his second-round match in straight sets Thursday, playing after getting an injection to numb the pain in his wrist.
But he said that he began "to feel more and more pain" overnight and could not move his wrist much Friday morning. Nadal added that he can no longer practice and wouldn't have been able to finish the tournament.
He said the problem is with the tendon sheath in his wrist and he was told that there is no way he could be given five more painkilling injections -- one before each possible match, were he to make it all the way to the final -- over the next 10 days.
Losing Nadal drains the French Open of more star power, following the pre-tournament withdrawal of 17-time major champion Roger Federer because of a bad back.
Nadal has ruled the French Open in a way no other man ever dominated any Grand Slam tournament. He is 72-2 at Roland Garros, winning four consecutive titles from 2005-08 and another five in a row from 2010-14.
"He's our biggest champion here," tournament director Guy Forget said.
Nadal's only losses came in the fourth round against Robin Soderling in 2009, ending a 31-match winning streak in Paris, and in the quarterfinals against Novak Djokovic last year, ending a 39-match run.
Nadal, seeded fourth this year, said he arrived in Paris before the French Open with "a little bit of pain" but that it progressively worsened. He won each of his first two matches in straight sets, including 6-3, 6-0, 6-3 against 99th-ranked Facundo Bagnis of Argentina on Thursday.
That made Nadal's career record in major tournaments 200-30, a winning percentage of .870. He is the eighth man in the sport's history to reach 200 match wins.
Nadal on withdrawal: If it wasn't Roland Garros I wouldn't have played
Rafael Nadal announces he is withdrawing from the French Open due to a wrist injury.