It happened on Hoyle Drive just before 7 a.m.
Pictures from the scene showed heavy damage from the ground floor of the building through the roof. Firefighters said there was also smoke damage to adjoining units.
By the time crews got the fire under control a total of 18 people were affected.
Fire investigators tell ABC11 just one unit was burned so badly that it's not safe for the resident to return.
The Red Cross is helping those displaced by the fire, including a woman who just got out of the hospital.
"I have two babies, and now I have nothing," Shonda Cotton said. "All of their clothes, my clothes, everything is just gone."
She says what she does have is support from her church - the Christian Missionary Faith Church of Raleigh. They are welcoming donations at 6512 Six Forks Rd, Raleigh, NC 27615.
Meanwhile, the cause of the fire is under investigation.