A government statement published in the Communist Party daily Granma says the two-story building contained two family homes.
The dead include a 3-year-old child, two 18-year-olds and a 60-year-old woman. Three other people sustained injuries that were not life-threatening.
Authorities said Thursday they were investigating what caused the structure's "total collapse" the previous day, including whether remodeling being done on the first floor was legal.
The colonial neighborhood contains most of Havana's oldest buildings.
Many are sorely decayed for lack of maintenance and vulnerable to structural failures that are regularly triggered by heavy rains.