The fire happened Sunday evening on Edinburgh Place in the College Park East neighbourhood.
Firefighters said they arrived to find smoke and flames coming from the building.
Everyone in the building had evacuated prior to crews arriving, fire department officials said.
Crews said they traced the fire to a unit on the fourth floor and brought it under control within 30 minutes.
The bodies of a cat and a large dog were found during a search of the unit, SFD officials said.
A fire investigator determined the cause of the fire to be accidental but said an exact cause is not available.
The building was deemed uninhabitable by the SFD until remediation occurs.
Saskatoon police assisted firefighters in allowing people back into their units to gather belongings before closing the building.
The SFD said a fire inspector will work with the property owner to monitor the progress of repairs.