"Kim had her baby," a hospital source told Us Weekly. "She's five weeks early. Kim got sick last night and had the baby early.
"They're all doing great and amazing!"
The 32-year-old reality television personality had the baby with boyfriend singer Kanye West, 36. She gave birth at Cedars-Sinai Medical Center in West Hollywood, Calif.
The magazine said Kardashian wasn't due until July 11.
Kardashian started dating in 2012 while she was still married to pro basketball player Kris Humphries. Their divorce was finalized June 4.
Celebrity Families of 2014 [PHOTOS]