The Dubai Civil Defense said the fire burned for at least two hours early Friday before firefighters started cooling the building.
There were no immediate reports of injuries, the Dubai Media Office tweeted
Video posted on social media showed fire on one side of the building and falling, flaming debris. The Torch Tower is near Dubai Marina.
Witness Samer Fathallah told CNN the fire engulfed 30 to 40 residences. Two cars in the parking deck were set ablaze by falling debris, he said.
Firefighters fought the fire from inside the building, and the crowd gathered 500 meters away could see water shooting out of the affected units.
Video posted on social media from a building across the street shows fire trucks arriving and debris covering the street. The flames in the video appear to shoot out of parts of the buildings on the middle floors.
The tower management company put out a statement saying all tenants had been provided accommodations in three hotels.
"Our team have spent most of today on the phone to tenants to check if they are in Dubai and some of our tenants are currently on vacation and were not present in the building," the company said.
Authorities said pets were saved and reunited with owners.
Tragedy strikes again
The Torch was the site of a massive fire in February 2015
The fire engulfed several floors on at least three sides of the iconic building. There were no deaths or injuries, and it was extinguished three hours after it began, the Civil Defense Office said.
The fire broke out in the early hours of the morning, when many people were out enjoying the nightlife in unseasonably warm temperatures.
Hundreds of people, many of whom were evacuated residents, were in the street while crews worked on the scene.
The cause of the 2015 fire is unknown.
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 682 residential units with 24-hour security and concierge, and six retail spaces. It has 84 floors, the developer's website says