Jovan Perkins sustained third-degree burns in the fire, which occurred before 2 a.m. Saturday. He was on life support, but died overnight.
The fire also killed the boy's mother, Millicent Brown-Johnson, the Chicago Tribune reported.
The Chicago Police Department's arson unit is investigating the cause of the fire, and a department spokesman said foul play is suspected due to evidence found at the scene.
When firefighters arrived at the scene, the top two floors of the three-story building were engulfed in the blaze, the Chicago Sun-Times said.
Brown-Johnson was in cardiac arrest and was taken to the hospital, where she died shortly after 3 a.m.