The six-story building Ningbo City collapsed around noon Sunday, Xinhua reported.
Residents of the building had recently complained of finding cracks in the walls. Most of them had moved out before the collapse.
Local officials said it was believed that only two women were in the building at the time of the collapse. One woman was pulled out, but died later at a local hospital. The other woman is still trapped in the debris.
Rescuers said the efforts to retrieve the second woman, who lived on the second floor, have been hampered by how deeply buried she is.
An investigation into the incident is under way.