There were no deaths or injuries, and the fire was out three hours after it began, the Dubai Civil Defense said.
The cause was not known, the Dubai Civil Defense said.
The fire started at 2 a.m. (5 p.m. ET Friday), when many people were out and enjoying the nightlife in unseasonably warm temperatures, witness Leah Polonenko said.
She shot video of the fire that showed flaming debris spilling from the 79-story building shortly after the fire started.
The fire appeared to start around the 50th floor, but then strong winds blew the burning debris around to lower floors on other sides, witnesses said.
At least four nearby buildings were evacuated as a precaution, Polonenko said.
Hundreds of people, many of them evacuated residents, were in the street while emergency crews were on the scene.
The Torch was the world's tallest residential tower when it was completed in 2011, according to the building's developer, Select Group. It contains 676 residential units with 24-hour security and concierge, and six retail spaces.
A resident of a nearby building told CNN he was watching a movie when he saw the fire.
"We went to the balcony, then it was one side of the building (that) was burning," Jaime Mueller, 30, told CNN by phone.
"We went downstairs and a lot of people were watching," he said. "Then we saw another piece of fire fall, and it started the fire on the other side."
The arc-shaped Dubai Marina is a popular and crowded residential area that has been developed rapidly in the past decade.