Firefighters evacuated residents from the fire floor as they battled the blaze.
Three other residents were taken to St. Joseph's Medical Center with smoke inhalation.
One man was rescued from a window of the apartment, and two others were helped down a stairway.
A firefighter who had burns to his face and another with a hurt shoulder were also taken to the hospital with non-life-threatening injuries.
Residents of the fire floor were evacuated and taken to a nearby shelter at 60 Temple Street used by emergency management.
The cause of the fire is under investigation.
