Nadal had just gone 5-1 up in the second set when a man wearing shorts and a white face mask with a red flare in his hand leapt out of the crowd near the umpire's chair and onto Court Philippe Chatrier.
He was not far away from Nadal but was quickly tackled by security staff and wrestled to the ground just off the court. Spaniard Nadal, who went on to win the title for a record eighth time, later shook the hand of a member of the security staff.
A few minutes earlier, play had been briefly interrupted when protesters high in the stands began chanting.
They were waving a banner saying in English, 'France tramples on children's rights', and it was believed the protests were co-ordinated by protesters opposed to gay marriage.
There were also protests on Roland Garros' second court, Suzanne Lenglen, where a group of men also wearing shorts and no shirts held up flares and a banner calling on President Francois Hollande to resign.
The same-sex marriage bill, which also legalises gay adoption, was signed into law by Hollande last month and a huge protest march took place in Paris on the first day of the tournament two weeks ago.
A spokeswoman for the France Tennis Federation said: "The incident is over and is now in the hands of the police."
It is the second time in five years an intruder has managed to get onto Court Philippe Chatrier during the men's final.
In 2009, a man dressed in a Spanish bullfighter's outfit was allowed to confront Roger Federer before being tackled by security staff.