Two of those killed were adults and the third was a child, according to police.
The fire on Dachauer Straße was sparked at around 2am. Four of those injured were taken to hospital due to smoke inhalation.
Munich-based newspaper the Süddeutsche Zeitung (SZ) reported that around 150 police, firefighters, and other emergency services arrived at the scene.
Firefighters worked for several hours to put out the flames in the building.
Due to the water used to put out the fire, the building is currently uninhabitable and the at least 97 people who lived there must find another place to stay, according to the SZ. The King's Hotel on Marsstrasse is being used as a shelter for many.
"My flatmate ran into my room. Smoke came in with him," one man named Adam told the SZ, explaining how the two escaped incoming flames by climbing out the window, along the roof and to a neighbouring building.
The cause of the blaze is not yet known.