Trouble erupted on Sunday in Frankfield Street, Cadowan, was more likely to be “rival gangs fighting” than anything related to terrorism, said police.
Emergency crews and a police helicopter were scrambled to the scene, where two vans had been set alight.
The three injured men are in a stable condition, Police Scotland said.
Det Supt Stephen Grant said: “Officers are continuing inquiries after three men were left injured in what we understand is a targeted attack in the Cardowan area. These three men are in a stable condition.
“This was a brazen incident on Frankfield Road, involving a number of vehicles being set alight.
“A substantial police response followed the initial reports.”
Neighbours told BBC Scotland reporter John McManus that the disturbance started at about 13:30.
Photographs posted by local residents on Facebook showed thick black smoke and two burnt-out vans being hosed down by firefighters.