"It happened on the sixth floor of the building where workers work, eat and sleep," a township official, surnamed Fang, told AFP news agency.
Safety and law enforcement officials have launched an investigation to determine what caused the fire, which was extinguished an hour after it broke out, Xinhua said.
Chen Zongfei, the owner of the factory, and his wife Huang Shubin, its manager, had been detained by police, Xinhua reported.
Zhu said that the couple had ignored two government directives to improve safety standards at the workshop.
Workshops in Fujian are often staffed by migrant workers from around the country in conditions that are often poorly regulated.
Accidents occur regularly across the country due to neglect of safety standards.
Many companies use poorly-maintained equipment and ignore environmental standards.
In a separate incident, at least 16 people were killed and 15 injured on Sunday in an explosion at a fireworks factory in Chongqing in southwest China.
China is one of the world's most dangerous places to work, with 320 people dying each day in work-related accidents, the government has said.