Garfunkel, 64, told People magazine his son, Beau, was born eight weeks ago in New York. The couple have another son, James, who was born in 1990.
"I'm doing pretty good," he said. "The baby's pretty good. We have good help."
The singer said he was getting ready to start work on a new album.
2014: The Year in Fashion [PHOTOS]
Polly Bergen, Emmy Award-winning actress, dies