"They have been keeping the baby a secret. They tried as soon as they were married. Zach is going to be an amazing father. They are looking to get a bigger place down the road," a source told Us magazine.
The 43-year-old actor, skipped out from attending the Toronto Film Festival where he was to promote his film "You Are Here", to be by his wife's side in the delivery room.
"Zach missed the premiere because his wife is very pregnant and about to give birth and he did not want to take the chance of not being in LA if she went into labour," the director of the film, Matthew Weiner said.
Galifianakis and Lundberg, the co-founder of the charity Growing Voices, tied the knot in Vancouver, Canada in August 2012.