The fire started on the second-floor of the 6-story building on Carpenter Avenue around 7:30 p.m. on Thursday.
It took firefighters just 40 minutes to get the blaze under control, but that was enough time to critically injure two people and seriously injure two others. One of the injured is a 1-year-old child.
The fire marshal is investigating the scene.
Several residents were forced to evacuate down their fire escapes.