The fire on the seventh floor at 1855 15th St. was first reported by fire officials on Twitter at 1:21 p.m. and was contained by around 1:50 p.m.
One person was helped out of the building and five in all were reported injured. None of the injuries were considered life-threatening, fire officials said.
Fire officials said they do not yet know if any residents will be displaced.
The fire's cause is under investigation and residents are being asked to avoid the area.
Stay with ABC7 News for the latest.