Abrahamian went into the next room and was talking to his fiancee on the phone when he collapsed, Harrison said. He was taken to a hospital, where he was pronounced dead.
Harrison says an autopsy was done Monday.
"It's a shock to everyone," Harrison told The Associated Press in a phone interview from the airport in Omaha, where he was waiting for Abrahamian's fiancee. They planned to get married in December in Hawaii, Harrison said.
Starship was the opening band for a concert that also featured Survivor and Boston.
Harrison said Abrahamian hadn't mentioned any health problems to him, but he apparently had been telling his fiancee.
"He had been having chest pains for a while," Harrison said.
Harrison said Starship's concert on Monday in Orem, Utah, was canceled.
Abrahamian joined Starship 11 years ago. Starship's history goes back to the 1960s with Jefferson Airplane and in 1980s Jefferson Starship.
Abrahamian lived in Austin, Texas. Funeral services are pending.