The landslides triggered by heavy rains struck just south of the city of Dingxi where Monday's earthquake left 95 dead, five missing and more than 800 people in hospital.
Nine villages under the city of Tianshui remained out of contact as of Saturday morning after the storms knocked out power, cut off communications and blocked roads, the official Xinhua News Agency said.
The heavy storms and mudslides left one village, Rongguang, filled with debris, damaging more than half of the village homes and burying villagers, Xinhua said.
The area along the Yellow River has rolling hills of loose soil blown south from the Gobi desert. Thunderstorms have loosened the terraced hillsides that were made unstable by the quake.
About 123,000 people were affected by the quake, with 31,600 moved to temporary shelters, the provincial earthquake administration said on its website. Almost 2,000 homes were destroyed and about 22,500 damaged, it said.
Urban areas where buildings are more solid were spared major damage, unlike the traditional mud and brick homes in the countryside.