Driver, however, did not reveal the father's name during her Thursday appearance on the show, People.com said.
The 38-year-old actress, who is best known for her roles in "Circle of Friends," "Good Will Hunting" and "The Phantom of the Opera," can now be seen on the FX series "The Riches."
The actress broke the news of her pregnancy after Leno teased her about gaining weight because she was spending too much time at buffets.
"Are you calling me fat? You've noticed my tummy, haven't you?" Driver challenged Leno, prompting him to ask if she is expecting.
"Yes, I am," she replied.
Driver said she is enjoying her pregnancy but having a tough time with morning sickness.
"I don't know why they call it morning sickness," she said. " I am sick morning, noon and night, but it's a fair trade-off."
Celebrity Families of 2014 [PHOTOS]