His leg was injured in the fall.
Others weren't so lucky. An Associated Press reporter saw a charred body partially hanging out one of the factory's barred windows. It appeared the victim tried to escape but couldn't make it through the bars.
"There were no safety measures taken in the building design. There was no emergency exit. All the people got trapped," said senior police official Amir Farooqi.
The factory's managers have fled and are being sought by police, said Sheikh, who is the senior government official in Karachi. He added that authorities have placed the name of the factory's owner on the list of people who are not allowed to leave the country.
Also on Tuesday night, a fire swept through a four-story shoe factory in the eastern city of Lahore, killing 25 people. Some died from burns and others from suffocation, said senior police officer Multan Khan.
The factory was illegally set up in a residential part of the city. The fire broke out when people in the building were trying to start their generator after the electricity went out. Sparks from the generator made contact with chemicals used to make the shoes, igniting the blaze.
Pakistan faces widespread blackouts, and many people use generators to provide electricity for their houses or to run businesses.
One of the workers, Muhammad Shabbir, said he had been working at the factory for six months along with his cousin. He said all the chemicals and the generator were located in the garage, which was also the only way out of the building. When the fire ignited, there was no way to escape.
Shabbir said he had just gone outside the factory when the fire started, but his cousin was inside and was severely burned. He died at the hospital.
A firefighter at the scene, Numan Noor, said the reason most of the victims died was because the main escape route was blocked.
"The people went to the back side of the building but there was no access, so we had to make forceful entries and . . . rescue the people," Noor said.
Firefighters broke holes in the factory's brick walls to reach victims inside. At the morgue, bodies were lined up on a hallway floor, covered with white sheets.
Pakistani Prime Minister Raja Pervaiz Ashraf expressed his shock and grief over the deaths in the two cities.