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.
The Spice Girl canceled her Wednesday night appearance on CNN's "Larry King Live."
According to Access Hollywood, the singer, whose real name is Melanie Brown, canceled because she and her new baby, Angel Iris Murphy Brown, are sick.
Brown was expected to discuss her paternity battle with Eddie Murphy over Angel for the first time in a televised interview.
"She canceled, but don't know why," a CNN spokeswoman told The ShowBuzz. "Not sure at this point when a reschedule date would be."
Instead of Brown's appearance, "Larry King Live" was to air interviews with family and friends of a young man murdered in the U.S. Virgin Islands, an update on the missing British child Madeleine McCann, and a report on various athletes who survived serious accidents.