The country's space station had two "close encounters" with Starlink satellites this year, Beijing claimed.
The incidents behind the complaints, lodged with the UN's space agency, have not yet been independently verified.
Starlink is a satellite internet network operated by Mr Musk's SpaceX.
Mr Musk is well known in China even as his electric carmaker Tesla comes under growing scrutiny from regulators.
The incidents occurred on 1 July and 21 October, according to a document submitted by China this month to the United Nations Office for Outer Space Affairs.
"For safety reasons, the China Space Station implemented preventive collision avoidance control," Beijing said in the document published on the agency's website.
SpaceX did not immediately respond to a request for comment from the BBC.
After the complaint was made public, Mr Musk, Starlink and the US were heavily criticised on China's Twitter-like Weibo microblogging platform.
One user described Starlink's satellites as "just a pile of space junk".
The satellites are "American space warfare weapons" and "Musk is a new 'weapon' created by the US government and military", others said.
Another posted: "The risks of Starlink are being gradually exposed, the whole human race will pay for their business activities."
China also accused the US of putting astronauts in danger by ignoring obligations under outer space treaties.
Foreign ministry spokesman Zhao Lijian said China was urging the US to act responsibly.
Scientists have voiced concerns about the risks of collisions in space and called on world governments to share information about the estimated 30,000 satellites and other space debris that are orbiting Earth.
SpaceX has already launched almost 1,900 satellites as part of the Starlink network, and plans to deploy thousands more.
Last month, the US space agency Nasa abruptly postponed a spacewalk from the International Space Station over concerns about space debris.
