The man, identified as Yonathan Souid, 23, from Esnandes in south-western France, faces charges of reckless endangerment and criminal trespassing.
He was arrested after jumping a fence and climbing up a beam on the famous bridge that connects Manhattan and Brooklyn, a police spokesman told AFP.
The incident occurred around 12:30 pm (1730 GMT).
Souid climbed back down at the request of a patrol officer who saw him and was detained.
He was due to be formally charged Monday, said a spokesman from the Brooklyn prosecutor's office, who added that he would remain in custody Sunday night.
"The Brooklyn Bridge must not be trespassed upon, no matter who does it or for any reason," said Brooklyn District Attorney Ken Thompson.
"In this age of terrorism, it's very important that we protect the security of the bridge at all times and under all circumstances," he added.
"This defendant blatantly compromised that security for his own selfish reasons and will now be prosecuted for his foolish and unlawful conduct."
This is the third similar incident at the Brooklyn Bridge in the last four months, in a city highly sensitive to security risks.
In late August, a Russian tourist, Yaroslav Kolchin, 24, was arrested and charged for climbing to the top of one of the towers supporting the mighty structure to take photos.
And in late July in the middle of the night, two German artists climbed to the top of the bridge to hoist two massive white flags in place of the US stars and stripes.
The appearance of the white flags prompted a police investigation, who ruled out any terrorist link.
The Berlin-based artists, Mischa Leinkauf, 37, and Matthias Wermke, 35, later claimed the stunt, saying they wanted to honor the beauty of public space.