Officers responded to reports of a stabbing at North Fourth and East Saint John streets just before 2 a.m. and learned the stabbing took place in a large parking garage nearby at Market and Santa Clara streets, said police spokesman Jermaine Thomas.
He said an altercation broke out between the three victims, ages 21, 23 and 39, and the suspect, and that the dispute escalated into a physical fight.
The three victims were taken to local hospitals to be treated for stab wounds that were not considered life-threatening.
Thomas said police received a phone call from another hospital around 3 a.m., reporting a man who matched the description of the suspect walked in with a non-life threatening stab wound.
Curtis Cooper, allegedly identified by witnesses and the victims as the suspect, was arrested on charges including assault with a deadly weapon.
It was not immediately clear how Cooper sustained his stab wound.
The incident remains under investigation.