The four buildings caved in during the early hours in Wenzhou in the eastern province of Zhejiang, the Lucheng district government said in a social media posting.
Eight people were found dead and five had been rescued by midday Monday, it said, without giving indications of the numbers missing.
The official Xinhua news agency said rescuers were still verifying the number of people trapped under the debris. It reported earlier on social media an "initial estimate" that more than 20 people had been buried.
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The cause of the collapse is under investigation.
Pictures from the scene showed workers in orange suits sifting through a mountain of ruins.
China has seen several building collapses in recent years, with some blamed 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.
Two people were killed and 24 injured in April when a storm brought down a wholesale market building in Foshan city, in the southern province of Guangdong.
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