The baby is the first child together for the couple after two years of marriage. They have name their newborn Dusty Rose Levine, reported People magazine.
The 37-year-old "Sugar" singer is currently taking a break from his tour with Maroon 5 to be with his wife and their baby.
The band recently cancelled their September 19 concert in Hartford, Connecticut and moved back several shows from late September this year to February and March in 2017.
"Sadly, it's par for the course with having a baby soon. It's life, and it's beautiful, but it can be complicated, and I apologize for any inconvenience," Levine had said.