The musician, who had played with Starship since 2000, was 46 when he died Sunday. He also performed with the rock bands Survivor, Toto, Loverboy and AC/DC.
"We are shocked and saddened at the sudden loss of our guitar player, Mark Abrahamian. We will miss you, brother," the band tweeted Monday. "Rest in peace, Mark."
UsMagazine.com said no other details regarding Abrahamian's death have been released.
Starship's planned concert in Orem, Utah, Monday was canceled.