Emergency services were called to Richmond Terrace, close to Avonmouth Docks, at about 20:30 BST, Avon and Somerset Police said.
One man was taken to hospital with serious injuries and he remains in a critical condition.
A second crew member, of the cargo ship that recently docked at Avonmouth, also required treatment but has since been discharged from hospital, while a third suffered minor injuries.
Supt Deepak Kenth confirmed all three men were Filipino nationals and said there had been a “suggestion racist language was directed towards at least one of the victims during the attack”.
Therefore, he said, police were “treating this as a suspected hate crime at this point, pending further information coming to light”.
He also addressed speculation online that the injuries were caused by a knife or similar weapon, but said this was not the case.