About 100 firefighters have been battling the blaze at the 36-storey Marco Polo tower in Honolulu since about 2pm local time.
The fire started on the 26th floor and eventually spread to the 25th floor and up to the 28th floor, according to fire department captain David Jenkins.
Mr Jenkins said at least three people were taken to hospital suffering from smoke inhalation and more were treated by paramedics at the scene. A total of 12 people needed medical help, he said.
Some residents in the 568-apartment tower are still unaccounted for and firefighters are going door-to-door in an effort to find them.
Meanwhile, glass and window frames were falling from the building, according to the Honolulu Star-Advertiser.
One resident said he reached safety after climbing the stairs from the 29th floor, where there was so much smoke he said he could hardly see.
Troy Yasuda, who lives in a building across the street, was giving water to people who evacuated.
He told the Associated Press: "They were choking from the smoke."
Police had been yelling through megaphones, telling those inside to come down, Mr Yasuda added.
Fourth-floor resident Aaron Dengler and his wife were helping their elderly neighbour get to an aid station set up at a nearby park.
He said: "It doesn't help to just stand and watch."
As he watched the flames spread, he said: "People are getting kind of nervous now. It's worrisome."
The Star-Advertiser said the apartment building was constructed in 1971 three years before sprinkler systems were made mandatory in such high-rises.
