The girl, Brown's second child, was born at 12.11am local time on Monday (1811 AEST) at St John's Hospital in Santa Monica.
"The baby is completely healthy with a good head of hair. No name has been decided on yet, and she is purely known as Baby Brown," the publicist added in a statement.
Mother and baby were now resting but face a looming paternity battle.
Brown says Hollywood actor Eddie Murphy is the father, a claim he disputes.
Brown, who performed under the name Mel B and was nicknamed Scary Spice, already has an eight-year-old daughter, Phoenix Chi, by ex-husband Jimmy Gulzar.