Two dozen workers were reported injured and dozens more trapped by thick smoke as rescue crews tried to reach them.
Witnesses said they saw a man fall from one of the 37-story building's upper floors, and hospital officials said that three hospitalised labourers were in serious condition.
There were no official reports of deaths, as police and fire officials refused to comment.
One man scaling the outside of the building got stuck on a narrow ledge on the 13th floor and was rescued after balancing on his precarious perch for more than an hour.
Rescuers eventually smashed windows to pull him to safety.
Trapped workers waved towels at hovering helicopters or climbed toward the roof on scaffolding.
Rescuers could be seen carrying injured workers on stretchers and putting them in ambulances.
Witnesses on the street below said the fire broke out around 12:30 local time (07:30 GMT) and burned for at least an hour before fire trucks arrived on the scene.
Attempts by Dubai's emergency services to extinguish the fire and rescue the trapped workers appeared disorganised.
A rescue helicopter was unable to land on the building's roof, and firefighters on the ground took hours to start evacuating workers out from a 10th story window, even after most of the smoke had dissipated.
It was not immediately clear why those trapped near the roof were unable to make their way to lower floors.
A hospital official, speaking on customary condition of anonymity, said up to 25 labourers from India, Pakistan and China were being treated for various degrees of smoke inhalation.