Flames tore through the four-story building on Hague Street around 1:45 a.m.
A dozen people, including one who was revived at the scene, were treated for smoke inhalation.
Dozens of others have been left homeless, officials said. The Red Cross was working to shelter those in need.
Fire investigators said the dead woman, whose name has not been released, was found on the second floor. They said she was in her late 50s and apparently had been dead for some time, although a cause of death was not known.
Investigators were working to determine the cause of the blaze, which apparently began on the first floor.
The fire was not considered suspicious.