The topless spectator wearing a white mask surged from the crowd near Nadal as the Spanish player was about to serve for the second set, leading 5-1. The man had the words "Kids right" written on his belly.
Security personnel bundled the man to the ground and quickly hauled him away.
Roland Garros tournament director Gilbert Ysern did not dwell on the matter.
"I have no wish to speak about it, quite honestly. The only thing I will (say) is that luckily our security services did a great job," Ysern said. "I don't want to give any additional publicity to these people, who, sadly, have a lack of a respect for sport and sportsmen. It's just pathetic."
The centre-court incident was one of several within the space of a few minutes by protesters. Police officials said a total of 12 people had been handed over by tournament security officials for questioning by police, but are not yet under arrest.
A guard stood near Nadal, protecting him, while the protester was subdued. Nadal took a couple of steps back to get away from the protester and, once the protester had been wrestled to the ground, shook the guard's hand before resuming play.
The match was only briefly delayed. Nadal beat David Ferrer 6-3, 6-2, 6-3 to win his eighth French Open title.
"I didn't lose my focus," Ferrer said. "Rafael, he was scared a little bit. But nothing happened, so it's okay."
Just ahead of the on-court protester being carried off, another protester could be seen a row or two back in the stands also being carried off.
Stewards also expelled a man and a woman from the Court Philippe Chatrier after they held up a banner that read in French: "Help! France is trampling on children's rights."
Another man and a woman held up a similar banner in English and shouted slogans.
"Today was strange," Ferrer said.
Five topless protesters also brandishing red flares and wearing white masks climbed to the top of the adjacent Court Suzanne Lenglen and unfurled a banner calling for the resignation of French President Francois Hollande.
Christophe Fagniez, the tournament's director of operations, said: "The situation is under control, it's in the hands of the police."
A male streaker wearing nothing but tennis balls and sneakers ran onto the centre court and hurdled the net during the 2003 final where Juan Carlos Ferrero beat Martin Verkerk.
In the 2009 final won by Roger Federer, a man jumped over the photographer's pit and ran on the court, went up to the Swiss player and tried to put a red hat on him. Federer brushed the man aside before security guards got close enough to intervene. After hopping the net, the man was tackled and jailed for questioning.
The worst incident involving an on-court intruder came in 1993 when a man reached over a courtside railing in Hamburg, Germany, and stabbed top-ranked Monica Seles between the shoulder blades. Seles returned to tennis in 1995, and won the 1996 Australian Open.
AP Sports Writers Jerome Pugmire, Howard Fendrich and Trung Latiuele contributed to this report.