Safety forces evacuated the building's 233 suites, primarily occupied by the elderly and disabled.
According to officials, the alarm sounded at 2:25 p.m. Firefighters arrived at 2:30 p.m. The fire was under control by 2:46 p.m.
The fire's cause was not immediately known.
The blaze began and remained in one apartment. Smoke could be seen billowing out the State Street side of the building.