The blaze at the facility in the city's Hiedingsfeld district broke out on the first floor, and police were alerted around 11:30 pm.
A 67-year-old man and a 70-year-old woman died at the scene despite attempts by rescue workers to revive them.
Fire fighters found the body of the 89-year-old woman who lived in the apartment where the fire began.
Among the six other residents injured, two were in critical condition, police said. Meanwhile, three rescue workers were also treated at a nearby clinic.
Nineteen residents of the first floor, some of whom were bedridden, were evacuated.
Some 50 fire fighters at the scene were able to control the blaze quickly, police said.