Videos online showed the training vessel Cuauhtemoc as it approached the iconic bridge over the East River, close to the Manhattan side of the span, which connects the borough with Brooklyn.
Its 45-metre masts were too tall to clear the arched bridge at that point and toppled when the vessel, named after the last Aztec emperor, sailed underneath.
Two of the four people who suffered more serious injuries later died, New York City Mayor Eric Adams said on social media early on Sunday morning, local time.
The cause of the collision is being investigated.
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.
The Mexican Navy said on social media late on Saturday that 22 people were injured on board the ship. It said 19 were receiving medical attention in local hospitals, including three with serious injuries.
No rescue operations were needed because no one fell into the water, it said.
Early on Sunday, Adams said on X that two of the 277 people on board at the time had died and two others remained in critical condition.
Naval cadets dressed in white uniforms could be seen dangling from the ship's crossbeams after the crash.
"No one fell into the water; they were all hurt inside the ship," a police official said.
The official said mechanical issues had probably caused the crash, without providing details.
At one of the suspension bridge's bases, near New York City's South Street Seaport, online video showed bystanders running in terror as the massive vessel hit the bridge and veered toward the dock.
The bridge, a popular tourist attraction and a main conduit between Manhattan and Brooklyn, was completed in 1883.
It was once the largest suspension bridge in the world.
The bridge did not sustain major damage, a New York City transportation official said.
Traffic reopened in both directions after a preliminary inspection.
In a post on social media, Mexico's foreign ministry said Mexico's ambassador to the US and other officials were assisting affected cadets and had been in contact with local authorities.
The training ship Cuauhtemoc was built at the Celaya Shipyards in Bilbao, Spain, in 1981, according to the South Street Seaport Museum.
The museum said on its website it was co-hosting the vessel's visit to New York, which had been scheduled to conclude on Saturday evening.
The public was invited to board the ship during its visit.
The ship was disembarking from New York and heading to Iceland, the New York police official said.
