The U.S. military said its destroyer, the USS Chung-Hoon, as well as a Canadian frigate were conducting a routine transit of the sensitive Taiwan Strait at the time.
In the video, the Chinese ship can be seen sailing across the path of the destroyer, which reportedly had to slow down to avoid a collision.
Canadian Navy Commander Paul Mountford witnessed the incident first-hand.
[HMCS Montreal Commander / Paul Mountford]
"The fact this was announced over the radio prior to doing it clearly indicated that was intentional.
"Manoeuvring close to each other, 150 yards is very scary, and you never want to be that close to another vessel because too many things can go wrong and you can actually have a collision."
China's military has rebuked the United States and Canada for the joint exercise, and on Monday Beijing said their ship operated in a legal and safe manner.
On Sunday, Taiwan's defense ministry called on China to respect the right to freedom of navigation.
China views Taiwan as its own territory, a claim the government in Taipei strongly rejects.
The incident comes as Beijing and Washington traded blame for not holding military talks. Tension between the two over trade, Taiwan and Russia's invasion of Ukraine have escalated in recent weeks.
This is the second such encounter in recent days. On May 26, the U.S. said a Chinese fighter jet carried out a "unnecessarily aggressive" maneuver near a U.S. military plane in international airspace over the South China Sea.
