Residents say they heard an explosion in the large building on Wardman Road just before the fire started early Monday.
Boston Fire Department spokesman Steve MacDonald tells the Associated Press that a man walked into a hospital with burns and told officials he started the fire.
MacDonald says the man was arrested. His name hasn't been released and investigators weren't sure if he lived in the building or was visiting.
Firefighters rescued about 15 people, including a 6-year-old boy who was dropped from a third-floor apartment into the arms of a firefighter.
MacDonald says 10 residents, two firefighters and one police officer were taken to hospitals.