The local government in Dingxi in Gansu province, where the 5.9- and 5.6-magnitude tremors struck, gave the figures on its verified social media account.
“More than 21,000 buildings were severely damaged and more than 1,200 have collapsed,” an official at the provincial earthquake bureau told AFP, adding that 371 aftershocks had been recorded.
The US Geological Survey said the initial 5.9-magnitude quake hit at 7:45 am (2345 GMT Sunday), with its epicentre 151 kilometres (94 miles) west of Beidao in Gansu at a depth of just 9.8 kilometres.
A second 5.6-magnitude tremor hit the same region at 9:12 am and was 10.1 kilometres deep, USGS said.
A resident of Min county told AFP he was at work at a medicine production plant when the tremor struck and he saw tower blocks shake “ferociously”.
“I was in the workshop. I felt violent shaking and so I ran to the yard of the plant immediately,” said the man, surnamed Ma.
“Our factory is only one floor. When I came to the yard, I saw an 18 storey building, the tallest in our county, shaking ferociously, especially the 18th floor.”
An official surnamed He from the Min county Communist Party committee told AFP there were more than 200 injured in seven affected townships in the area.
While Gansu is one of China’s more sparsely populated provinces, Dingxi city, which includes the worst-hit counties, has a population of about 2.7 million.
A report on the 163.com Internet news portal said 500 troops, including 120 specialised rescuers were on their way to the disaster zone.
Pictures broadcast on state television showed rural villages with rubble-strewn streets.