The fire occurred in the 13600-block of South Lamon Avenue just west of Cicero Avenue.
At least one person had to be transported to the hospital because of smoke inhalation, authorities said.
The fire was contained to a single unit in the building. The cause of the fire is under investigation.
A cat was having trouble breathing as well and firefighters were seen giving the cat an oxygen mask.
Eight people have been displaced by the fire. The Red Cross is helping them with housing.