The incident about nine minutes after the launch of the Chang'e-3 mission early Monday happened in Suining county in the central province of Hunan, which has been hit by space wreckage nearly 20 times, the Xiaoxiang Morning Post said.
"Three of the roof beams have crashed down on our house, and a big hole has been punched into our barn," one local resident told the paper.
"The huge sound scared the living daylights out of me," said another.
A picture showed a somewhat baffled-looking villager peering at the curved shape of what appeared to be a rocket nose-cone, below a gaping hole in his roof.
Authorities gave the residents 10,800 yuan ($1,800) and 5,200 yuan in compensation, the paper said. No one was injured.
A Long March-3B carrier rocket, China's most powerful such vehicle, blasted off at around 1:30 am Monday from the Xichang Satellite Launch Centre in southwestern China.
The lunar rover mission is part of China's ambitious space programme, which has the goal of establishing a permanent space station by 2020 and eventually sending a human to the moon.
But debris from China's numerous space launches has frequently found its way to Suining county, which has been hit by rocket parts nearly 20 times since the early 1990s, the Xiaoxiang Morning Post reported.
Last May wreckage from a rocket sent up by the Xichang Launch Centre crashed into homes and hit a high-voltage wire in the area, according to the Shanghai Daily News.
In October 2011 a steel frame weighing more than 250 kilograms (550 pounds) landed in a field after another satellite launch, and other wreckage pierced a house roof.