The incidents are said to have occurred on July 1st and October 21st, involving the Tiangong station, which contains a crew of three.
Beijing has accused Washington of ignoring its treaty obligations to ensure no harm comes to the station and its crew.
In a complaint lodged to the UN Committee on the Peaceful Uses of Outer Space, Beijing said its station was forced to take "evasive manoeuvres" to "prevent a potential collision" with the Starlink satellites launched by Musk's Space Exploration Technologies.
Foreign ministry spokesperson Zhao Lijian has called on the US to "take immediate measures to prevent such incidents from happening again."
Lijian said Washington had failed to "protect the safety of astronauts," as agreed in a 1967 treaty on the use of space.
China launched the Tiangong station in April for an initial 90-day mission. A second, current six-month long mission was launched on October 16th with a crew of two men and one woman.
SpaceX's Starlink satellites are part of a project to bring internet access to previously overlooked parts of the world. The project will see the launch of over 2,000 satellites in total.
