Shenzhen is just over the border with Hong Kong in Guangdong province.
The official Xinhua News Agency said the fire broke out in a club called "King of the Dancers" while hundreds of people were watching a show.
An initial police investigation showed that the blaze was triggered by fireworks ignited during the show, Xinhua said.
Many partygoers were hurt in a stampede to escape down "a narrow aisle," a club staff member was quoted by the agency as saying.
"I saw people rushing out ... and all the lights were off," it quoted Yang Zhi as saying. Xinhua said Yang suffered burns to his neck.
Fires and accidents in bars, theaters and other public places are common in China despite government pledges to improve safety. Many are caused by negligence and lax safety procedures, such as a lack of fire extinguishers and emergency exits.
In China's worst recent nightclub disaster, a fire blamed on a welding accident tore through a disco in the central city of Luoyang in December 2000, killing 309 people.
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