The child will be the first for the couple who married in June after about three years of dating.
"(They) couldn't be more thrilled," Schwimmer's publicist told People.com.
The baby's gender and anticipated due date were not reported.
Schwimmer is best known for his work on TV's "Friends" and in the animated "Madagascar" movies. He also recently directed the big-screen comedy "Run, Fat Boy, Run."