Passengers aren't strapped in on the ride, and the 25-year-old man apparently jumped out of his train car, with a leap powerful enough to clear the perimeter fence.
Details of what happened next were unclear, but police said the tiger attacked. The zoo's staff used a fire extinguisher to chase the tiger off, and the man was instructed to roll under a electrified wire to get to safety, zoo director Jim Breheny said in a statement. Zookeepers then called the tiger into a holding area.
The man was conscious and talking after the mauling, Breheny said.
"If not for the quick response by our staff and their ability to perform well in emergency situations, the outcome would have been very different," he said.
Police said the man was hospitalized in critical condition.
The Bronx Zoo, one of the nation's largest, sprawls over 265 acres and contains hundreds of animals, many in habitats meant to resemble natural settings. Its exhibits include Tiger Mountain, Congo Gorilla Forest and World of Reptiles.