The 31-year-old Brown, known as Scary Spice when she was in the megahit group of the '90s, gave birth to the child April 3 in Santa Monica, Calif.
Brown's publicist, Nadine Bibi, didn't immediately respond Friday to an e-mail from The Associated Press asking for details.
Arnold Robinson, a spokesman for Murphy, declined comment.
Brown has said ex-boyfriend Murphy is the father. The 46-year-old "Dreamgirls" star has said he isn't sure, while Brown has said there is "absolutely no question that Eddie is the father."
Brown has an 8-year-old daughter, Phoenix Chi, from her marriage to Jimmy Gulzar.
Murphy has five children from his marriage to Nicole Mitchell Murphy.