Rescuers were still verifying the number of people trapped in the debris in Wenzhou's Lucheng industrial district. An initial estimate was that more than 20 people had been buried, the state-run Xinhua news agency reported.
Eight persons were found dead while 13 others have been rescued, it said.
The cause of the collapse was under investigation.
Several buildings have collapsed in recent years mainly due to on low quality construction.
In May, 16 people were reported dead after a residential building in Guizhou province in the southwest collapsed due to landslides.