The incidents reported by Beijing to the United Nations (UN) space agency have not been independently verified.
The incidents occurred on July 1 and October 21, according to documentation submitted by China to the UN.
“For security reasons, the Chinese space station implemented a preventive control to avoid collisions,” Beijing said in the complaint.
SpaceX did not immediately respond to the BBC’s request for comment.
Once the incident was known, Musk, Starlink and the United States received numerous criticisms on the Chinese social network Weibo.
“The risks of Starlink are gradually being exposed. All humanity will pay for their economic activities,” said one user.
China also accused the United States of putting astronauts at risk by ignoring outer space treaty obligations.
Foreign Ministry spokesman Zhao Lijian said China calls on the United States to act responsibly.
Scientists have made public their concern about the risks of collisions in space and have called on world governments to share information about the 30,000 satellites and other space debris that are estimated to orbit Earth.
SpaceX has already launched nearly 1,900 satellites as part of its Starlink network to provide low-cost Internet and plans to put thousands more into orbit.
Last month NASA postponed a spacewalk from the International Space Station at the last minute because of the risk of collision with space debris.
Elon Musk has announced the arrival of Starlink in beta mode.
Melissa Galbraith is the World News reporter for Globe Live Media. She covers all the major events happening around the World. From Europe to Americas, from Asia to Antarctica, Melissa covers it all. Never miss another Major World Event by bookmarking her author page right here.