The first earthquake near Dingxi city had a magnitude of 5.98 and was shallow, with a depth of just 9.8 km (6 miles), the US Geological Survey said
Just over an hour later, a magnitude 5.6 quake hit the same area, it added.
In 2008, an earthquake in Sichuan province left up to 90,000 people dead and millions homeless.
A factory worker in Min county told AFP that he felt “violent shaking” and “ran to the yard of the [factory] plant immediately”.
“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,” he said.
The area has been hit by 371 aftershocks, according to the Earthquake Administration of Gansu province.
Tremors were felt in the provincial capital, Lanzhou, and as far away as Xian, 400km (250 miles) to the east.
At least 5,600 houses in the province’s Zhangxian county are seriously damaged and 380 have collapsed, while some areas suffered from power cuts or mobile communications being disrupted, the earthquake administration added.
“Many have been injured by collapsed houses,” a doctor based in Minxian county was quoted by Reuters news agency as saying. “Many villagers have gone to local hospitals along the roads.”
The earthquake has caused a direct economic loss of 198 million yuan ($32m; £21m), the Dingxi government said on its microblog.
Both the Chinese President Xi Jinping and Premier Li Keqiang had called Gansu province to express their concern for the victims and stress the importance of the rescue operations being conducted well, the Dingxi government added.
Crews of fire fighters and rescue dogs have already arrived at the scene, the BBC’s Celia Hatton in Beijing reports.
The closer to the surface an earthquake strikes, the more damage it can cause, our correspondent adds.
The earthquake reportedly triggered a series of mudslides and landslides, making it difficult for rescuers to access some areas hit by the quake.
The Gansu military police have deployed 500 soldiers, including 120 specialist rescuers, while 500 emergency tents and 2,000 quilts are also being transported to affected areas, Xinhua added.
Officials from the civil affairs, transportation and earthquake departments were also visiting local towns to assess the damage, a statement on the Dingxi party website said.
Rain is expected in the region later, leading to fears that this will make rescue efforts more difficult, or cause more landslides.
“Showery weather is expected tomorrow, and lighter rain the day after that. The rain may have an adverse effect on rescue efforts – please pay attention and be on guard!” the Dingxi government wrote on its microblog.
Residents in towns near the earthquake also reported feeling the tremors.
“You could see the chandeliers wobble and the windows vibrating and making noise, but there aren’t any cracks in the walls,” AP news agency quoted a clerk at Wuyang Hotel, about 40 km (25 miles) from the epicentre, as saying.
“Shop assistants all poured out onto the streets when the shaking began,” the clerk said.
Major recent earthquakes in China
- April 2013 – 6.6 magnitude quake in Sichuan province kills at least 160
- September 2012 – 5.6 magnitude quake in south western Yunnan and Guizhou provinces kills at least 80
- March 2011 – magnitude 5.4 earthquake in Yunnan kills at least 22
- April 2010 – magnitude 6.9 quake hits Qinghai province, killing over 1,100
- May 2008 – magnitude 7.9 earthquake in Sichuan kills up to 90,000
- April 20 2013 China quake kills scores in rural Sichuan (chinadailymail.com)
- May 16 2008 Five Million Homeless After Chinese Earthquake (chinadailymail.com)
- July 28 1976 Worst modern earthquake hits Tangshan, China (chinadailymail.com)
- Earthquake in China kills at least 47 in Gansu province (metro.co.uk)
- China’s Gansu hit by deadly quake (bbc.co.uk)
- At least 22 killed in NW China earthquake – Xinhua (news.xinhuanet.com)
- China’s Gansu province hit by powerful earthquake (sott.net)
- Earthquakes in China’s Gansu province (indiavision.com)
- 11 killed as 6.6 magnitude earthquake hits western China (thehindu.com)
- At least 3 dead after shallow 5.9 quake hits China (foxnews.com)
- 6.6 magnitude earthquake hits China’s Gansu province (thehindu.com)
- China launches emergency-response to Gansu quake – Xinhua (news.xinhuanet.com)
- Strong earthquake in western China kills 47 people (news.yahoo.com)