Eight others were injured, three critically, in the blaze that began in the basement of a four-storey building in the northern Bourtzwiller district, the fire service said.
Reports said that three of the victims were of Turkish origin. The fire broke out at a neighborhood where many Turks live.
The fire broke out shortly before midnight.
Around 20 residents were rescued from their homes by ladder, the local l'Alsace newspaper reported.
"It's terrible, the whole city has been shaken by this tragedy," Mayor Jean Rottner told AFP.
The cause of the fire was unknown.
"The building is in very good condition and is situated in a quiet housing project, with no particular problems," Rottner said.