Another person was wounded and hospitalized.
Police said the triple homicide-suicide took place at a Brooklyn building where at least some of the band members were thought to have lived, the New York Post reported.
The gunman, carrying a Century Sporter .308-caliber semiautomatic rifle with a 20-round magazine, fired at a person standing outside of the apartment building, wounding him, and went inside, killing two people on the first floor and one on the third, police said.
The man then went to the roof of the building and shot himself, police said.
Police said the building was littered with spent shells.
The band's members are Iranians who had been in the United States for an undetermined length of time and were seeking asylum, law enforcement sources told the Post.
Police were called to the scene on reports of shots fired and heard more shots when they entered the building, WABC reported.
A neighbor, identifying himself as Frank, told the Post the building was the site of several rowdy parties.
"During the summer it was ongoing; really loud parties with the street blocked off by gypsy cabs," he said. "It was the usual hipster rave scene."