Nathaniel Glover, known as The Kidd Creole, was detained on Wednesday over the fatal stabbing of a 55-year-old man in Manhattan the previous evening.
Mr Glover allegedly had an argument with the victim, local media report.
His group, which formed in 1976, found fame with the song The Message in 1982.
The victim, later identified as John Jolly, was found with multiple stab wounds in Midtown Manhattan after police received an emergency call shortly before midnight on Tuesday, the New York Police Department said.
Mr Jolly, who police said lived in a shelter, was taken to Bellevue Hospital, where he was pronounced dead a short time later.
Mr Glover, 57, lives in the Bronx and works as a handyman and security guard near the scene of the stabbing, according to the New York Daily News.
His band, which was formed in the South Bronx, consists of five other members; DJ Grandmaster Flash, Melle Mel, Keith Cowboy, Scorpio (aka Mr Ness) and Rahiem.
Hits include the 1982 rap single The Message and White Lines (Don't Don't Do It), released in 1983.
In 2007, Grandmaster Flash and The Furious Five became the first hip hop group to join the Rock and Roll Hall of Fame.
A founding member of the 1980s hip hop group Grandmaster Flash and The Furious Five has been charged in connection with the killing of a homeless man in New York City, police say.