The top of the ship's three masts slammed into the iconic span, partially collapsing as the boat floated in the East River.
At least 22 people were injured, three critically, in the accident, according to a statement from the Mexican Navy.
"No personnel fell into the water, so it was not necessary to activate rescue operations," the statement added.
Meanwhile, New York City Mayor Eric Adams said that 19 people were injured in the crash, four of them seriously, but the 142-year-old bridge was spared major damage. The cause of the collision is under investigation.
What else do we know about the crash?
Multiple eyewitness videos captured the masts snapping and partially collapsing as they crashed into the bridge's deck. Videos showed heavy traffic on the bridge at the time of the collision.
The vessel then drifted toward the river's edge as onlookers scrambled away from the shore. Sailors could be seen aloft in the rigging on the damaged masts.
The New York Post reported that victims were rushed to local hospitals.
According to multiple US media reports, around 200 people were aboard the Cuauhtemoc, a barque built in 1982 with a mast height of 48.2 meters (158 feet) at the time.
The Cuauhtemoc had been on a training maneuver at the time and was damaged in the "mishap," according to a separate statement by the Mexican Navy on X.