Lyla Rose Loeb Hershkovitz arrived Sunday morning at Cedars Sinai Medical Center in Los Angeles and is the first child for the couple.
Loeb, 41, and Hershkovitz, 31, a music production supervisor for The Tonight Show with Conan O'Brien, announced that they were expecting in September.
The couple met in 2006 at a business meeting and married last January.
Loeb shot to fame in 1994 with the No. 1 single "Stay (I Missed You)" from the movie Reality Bites.
She also helps underprivileged children through her own non-profit, the Camp Lisa Foundation, which gives at-risk kids the chance to go to summer camp. Her latest CD, Camp Lisa, is available now.
Additionally, Loeb's latest project – the Lisa Loeb Eyewear Collection from Classique Eyewear – is due out in spring 2010.
Reporting by ELIZABETH LEONARD