The fire broke out at 1882 Grand Concourse around 1 p.m. on Tuesday.
Some 140 firefighters responded to the scene.
The fire started on the seventh floor of the 11-story building, forcing approximately 70 people out of their homes.
Twenty-five units were placed under a vacate order, and Red Cross opened a reception center at nearby Mount Hope Community Center.
The residents are being comforted with a warm place to stay, food, beverages and health and mental health services.
Five people suffered minor injures and were taken to Lincoln Hospital.
The cause of the fire is still under investigation.