"Mother and daughter are healthy and resting comfortably. Everyone's very happy," says the actor's rep, Matt Labov.
Kinnear, who turns 43 on Saturday, will be seen in the upcoming Fast Food Nation, which premiered at last month's Cannes Film Festival. He and writer and former model Helen, 36, were married in 1999.
Their first child, Lily Kathryn, was born in 2003.