The quake hit near the city of Dingxi in Gansu province, a hilly region of mountains, desert and pastureland about 1,233 kilometers (766 miles) west of Beijing.
Residents described shaking windows and swinging lights but there was relatively little major damage or panic in the city itself. Tremors were felt in the provincial capital of Lanzhou 177 kilometers (110 miles) north, and as far away as Xi'an, 400 kilometers (250 miles) to the east.
The government's earthquake monitoring center said the initial quake at 7:45 a.m. (2345 GMT Sunday) was magnitude-6.6 and subsequent tremors included a magnitude-5.6.
The quake was shallow, which can be more destructive. The center said it struck about 20 kilometers (12.4 miles) beneath the surface, while the Gansu provincial earthquake administration said it was just 6 kilometers (3.7 miles) deep.
The U.S. Geological Survey measured the magnitude of the initial quake as 5.9 and the depth at 10 kilometers (6 miles).
Initial measurements of an earthquake can vary widely, especially if different monitoring equipment is used.
The deaths and injuries were reported in Min County and other rural southern parts of the municipality, Dingxi Mayor Tang Xiaoming told state broadcaster CCTV. Tang said damage was worst in the counties of Zhang and Min, where scores of homes were damaged and telephone and electricity services knocked out.
Su Wei, leader of a 120-member rescue team from the paramilitary People's Armed Police, told state broadcaster CCTV that they were on their way to the epicenter, but progress was being slowed by mud and rock slides blocking the road.
The Chinese Red Cross said it was shipping 200 tents, 1,000 sets of household items, and 2,000 jackets to the area and sending teams from both Lanzhou and Beijing to help with relief work and assess further needs.
Heavy rain is expected in the area later in the week, raising the need for shelter and increasing the chance of further landslides.
More than 1,200 homes were destroyed by the quake, with another 21,000 badly damaged, provincial government spokesman Chang Zhengguo was quoted as saying by the official Xinhua News Agency.
With a population of 26 million, Gansu is one of China's more lightly populated provinces, although the New Jersey-sized area of Dingxi has a greater concentration of farms in rolling hills terraced with fields for crops and fruit trees. Dingxi has a total population of about 2.7 million.
China's worst earthquake in recent years was a 7.9-magnitude temblor that struck the southwestern province of Sichuan in 2008, leaving 90,000 people dead or missing.