The fire happened in the 2900 block of South State Street, Chicago Fire Department officials said. The six-story building is in the Dearborn Homes area and is owned by the Chicago Housing Authority.
The use of fireworks caused a mattress to catch fire inside the building, officials said.
Firefighters responded to the fire, located on the building's fourth floor, and extinguished it.
One child who was injured in the fire had minor burn injuries, officials said. The two other injured children were being treated for smoke inhalation. All three children were taken to Comer Children's Hospital in good condition.
The ages of the children were not immediately known.
No further details were available.