Wearing a red shirt and carrying a red and blue flag, the intruder made a beeline for Federer as Soderling was getting ready to serve at 2-1 down in the second set.
The startled world number two backed away and the man ran around court and jumped over the net before he was rugby tackled by security guards.
"I didn't know exactly what happened. All of a sudden I heard the crowd, and I looked over and he jumped over the fence or something," Federer said after winning his first French Open title.
"That gave me a fright, just like seeing him so close right away."
The incident again highlighted how easy it is to breach security at tennis tournaments, especially since it is supposed to have been tightened after Monica Seles was stabbed in the back by a Steffi Graf fan at a Hamburg tournament in 1993.
"The good thing is like it happened before so that's why I guess I didn't panic," added Federer.
"It happened in Wimbledon before when two guys ran out on the court, and once I think it was in Montreal when I lost to Roddick when I was playing for my number one ranking in the third set.
"This guy, I don't know, he looked at me and I was not sure what he wanted. It seemed like he wanted to give me something.
"So I was actually okay, because I saw he wasn't pulling for anything stupid. It definitely felt uncomfortable once he came close to me."
The man was on court for only 18 seconds but he had done enough to rattle Federer, who promptly lost three points in a row.
"Looking back, it definitely threw me out of my rhythm a little bit. One game later I thought that maybe I should have sat down and taken a minute or two to kind of reflect on what just happened," Federer explained.
His Swedish opponent was left bewildered as he watched the man running around the court.
"It wasn't really a nice thing to see. I think the security was at least as surprised as we were. It's very bad that things like this can happen," Soderling said.
In another famous incident, a female streaker ran on to Wimbledon's Centre Court just before the 1996 men's final between Richard Krajicek and Malivai Washington.