Murphy acknowledged his paternity of Brown's daughter, Angel, last week, one day after the 32-year-old singer took legal action to establish him as the parent.
Belafonte is a movie producer whose recent credits include "Sisters" and "Thank You for Smoking." Brown was known as Scary Spice when she performed with the Spice Girls, whom she'll join for the band's reunion tour in December and January.
A marriage certificate filed with Clark County, which encompasses Las Vegas, lists the date of the couple's nuptials as June 6. It does not state exactly where they were married.
An email to Brown's publicist was not immediately returned.