Nearly 50 Phoenix firefighters responded to the blaze near 36th Street and Earll Drive about 1:20 p.m. Wednesday.
Crews say flames were coming out the windows on the bottom floor when they arrived at the scene.
Firefighters say a 10-month-old boy and a 2-year-old girl who were on the first floor suffered from smoke inhalation and sustained minor burns.
The Arizona Republic says both children were taken to a hospital. Their names haven't been released.
Crews contained the fire within 20 minutes. The blaze left extensive smoke and fire damage in two apartments plus water damage in the adjacent apartment. The cause of the fire hasn't been determined yet.