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 wrestled the man to the ground and quickly hauled him away.
"I felt a little bit scared at the first moment because I didn't see what's going on. I just turned there and I watch a guy with some fire," Nadal said. "It's one of those things that nobody can prevent."
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 center-court incident was one of several within the space of a few minutes by protesters. Police officials said 12 people had been handed over by tournament security officials for questioning by police. Seven were held in custody for further questioning for bringing flares into Roland Garros and the other five were released.
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.
"Thank you very much to all the security guys. They did just amazing work," Nadal said. "They (were) very quick and they were very courageous."
The match was delayed only briefly. 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 OK."
Just before the on-court protester was carried off, another protester could be seen a row or two back in the stands also being removed.
Security officers also expelled a man and a woman from the Court Philippe Chatrier after they held 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.
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.