Videos online showed the ship sailing underneath the bridge connecting the New York City boroughs of Brooklyn and Manhattan, as its masts struck it.
New York City Mayor Eric Adams said the 142-year-old bridge was spared major damage but at least 19 people on board the ship needed medical treatment after the crash.
Two of the four people who suffered more serious injuries later died, Adams announced on social media early on Sunday morning, local time.
The cause of the collision was under investigation.
Videos showed heavy traffic on the span at the time of the Saturday night collision.
The vessel, which was flying a giant green, white and red Mexican flag and had 277 people aboard, then drifted toward the piers lining the riverbank as onlookers scrambled away.
Many people, dressed in what appeared to be white sailor uniforms, could be seen dangling from the ship's crossbeams.
At the base of the bridge, bystanders could be seen running away from the approaching ship.
The Mexican Navy said in a post on the social platform X that the Cuauhtemoc, an academy training vessel, was damaged in an accident with the Brooklyn Bridge that prevented it from continuing its voyage.
It added that the status of personnel and material was under review by naval and local authorities, which were providing assistance.
The Foreign Affairs Ministry said on X that its ambassador to the US and officials from the Mexican consulate in New York were in contact with local authorities to provide assistance to "the affected cadets".
With AP
6°C