“There was only a narrow aisle … in the hall. Many people got hurt in the stampede,” Yang Zhi, a staff member, was quoted as saying.
Shenzen, which is in the province of Guangdong, lies close to China’s border with Hong Kong.
Wang Yang, Guangdong province’s Communist party secretary, ordered that families of the victims be “appeased” and “social stability” maintained, the China News Service said.
He called for the authorities to quickly find those responsible.
Outbreaks of fire are common in China, where the fire and safety laws are widely contravened.
The Chinese government said earlier this year that 1,418 people had died and 863 had been injured in fires in 2007.
But the toll could be higher as local officials are known to have covered up accidents to avoid punishment by the authorities.
In October 2007, 37 people were killed in a fire in a shoe factory in Fujian province. In 2000, 311 people died in a fire at a nightclub in the central city of Luoyang.