The building in Guiyang, the capital of Guizhou province, collapsed around 11:30 am.
The city government said it had checked three-quarters of the 35 households and found at 21 of the 114 residents were missing.
It said that heavy rainfall led to the collapse of the building.
Ninety-three of the residents have been confirmed safe.
A man surnamed Zhang who lived on the ground floor was pulled out by rescuers.
Also Read
He told state-run Xinhua that he was awakened by loud noises. He was about to run when he was covered by falling debris.
"She lived on the ninth floor," she said.
"I called, but couldn't reach her."
Residents of nearby buildings were also evacuated after the accident.