One of the victims was stabbed in the back of the head and was taken to Harborview Medical Center with life-threatening injuries. The other man was stabbed in the shoulder and is expected to recover.
Police spokesman Jeff Kappel said officers have arrested a suspect, but it was not clear what prompted the attack or if the man knew the victims, who are both in their 30s.
The stabbing happened about 8:20 p.m. near the intersection of Beacon Avenue South and South Graham.
Kappel said the attacker got up from his seat and stabbed the two men as they were walking past him toward the bus door.