The fire started at 5.04am (NZ time), according to Sharjah Civil Defence teams.
A resident told the Gulf News it started on the 10th floor: "It was a small fire to begin with and we came out of the building as soon as we saw it."
Another local said he stepped out on his balcony when he heard the sirens: "It was such a gory sight. Carpets on fire were falling from balconies. Curtains too. I am standing down to see if we can help people out."
Colonel Dr Ali Abu Al Zoud, from Sharjah Police said that police used a drone to check for residents trapped inside the building.
Al Zoud told the Gulf News: "We have contacted the building owner and alternate accommodation will be provided to all residents. It is still not clear how many apartments have been affected."