Fire crews were called to the complex in the 600 block of Peyton Street, off Martin Luther King Jr. Boulevard, just after 11:30 p.m.
When they arrived at the scene, flames were seen shooting from the windows on the top floor.
About 13 people were hurt as they fled the building. At least seven of them were injured after jumping from the third floor to safety. They were taken to the hospital, but the extent of their injuries are unknown.
A 12-year-old girl who was inside the building when the fire broke out said her dad jumped out of a third floor window, grabbed a ladder from his work truck, and went back to the building to rescue his family.
"I was glad that he got it," Lizet Cruz said. "I was glad that nothing happened to him, because that smoke was like, really strong ... I thought something was going to happen to [my family]. My mom was crying like something happened to her so I was really, really scared."
A resident in a neighboring apartment building also ran over to help several tenants escape.
"You can see that ladder right there, I was at the bottom of it, trying to help babies get out the building," Malik Ray said. "A lot of kids. There was a lot of commotion, I wasn't really sure. I was just trying to help everybody get out of the building."
Despite firefighters getting the blaze under control by midnight, the building sustained heavy damage. At least 12 apartment units were damaged, according to authorities.
The Red Cross has been called in to help over 50 displaced residents.
Meanwhile, the cause of the fire is still under investigation.