The fire broke out around 2 p.m. Thursday on Lexington Avenue.
Fire officials say the upper floors were fully engulfed when firefighters arrived.
Residents were struggling to escape the flames.
"When firefighters arrived, people were trying to escape the fire, escape the building I should say, they rescued a woman in the rear of the building via ground ladder, and also other people were evacuated from the structure by police," Clifton Fire Department Chief Frank Preziosa said.
One resident was taken to the hospital with non-life-threatening injuries.
Several police officers suffered smoke inhalation while helping residents out of the building.
The Red Cross was providing temporary lodging, food and clothing for 21 people from four different families who were displaced.
----------
* Get Eyewitness News Delivered
* More New Jersey news
* Send us a news tip
* Download the abc7NY app for breaking news alerts
* Follow us on YouTube