Aiden Bice was born Saturday. No other details were immediately available.
The couple, who have been together two years, got married in their home state of Alabama on June 15.
Fisher and Bice met before the singer stole the spotlight on FOX's talent hunt – when he worked as a guitar store clerk and frequented the Ragtime Cafe in Hoover, Ala., where she waited tables.
Bice, 29, finished in second place on last season's Idol, behind Oklahoma native Carrie Underwood. But being a runner-up hasn't hurt Bice's career: He signed a record deal with RCA less than 24 hours after the Idol finale and his single of the show's original song "Inside Your Heaven," topped the charts. His debut album is due out Nov. 29.
Meanwhile, Bice also recently made a personal contribution to Hurricane Katrina victims, temporarily donating his Helena, Ala., home to a New Orleans family left homeless by the floods.
"I wanted to do anything I could," Bice told PEOPLE. He planned to live in Nashville and work on his recording career while the Booth family – two attorneys and their two children – planned to stay in Helena for six to eight months.