The "Circle of Friends" and "Good Will Hunting" actress did not say what the man's name was, but said he had been part of the writing team of her former show, UsMagazine.com said.
"I don't need to protect him anymore," Driver told the British newspaper The Observer.
"He can fend for himself. He's a grownup. We weren't together and he wasn't directly in the business so I chose to protect him and not have a rain of publicity. ... He's not famous. ... There's no big story."
As for what kind of father the mystery man is, Driver said: "Is he a good dad? Sort of. He's figuring it out. ... I mean, he hasn't been that involved -- his choice. But he is now."