The incidents began Friday just before noon, when 56-year-old man hopped over a wooden fence and made his way through a restricted area toward the snow leopard enclosure, according to an NYPD spokeswoman.
Zoo staffers escorted him out and took away his season pass, police said.
The next day, a 37-year-old New York Post reporter went into the same area, the Himalayan Highlands exhibit, and tried to access the red panda enclosure, according to the NYPD.
She was given a summons for trespassing, police said.
Zoo officials declined to comment on the incidents.
In a statement a New York Post spokeswoman said that the reporter did not break into or access the zoo exhibit.
"While covering the story about the man who tried to jump into the snow leopard exhibit, she inadvertently crossed a strip of grass that was not clearly labeled," the spokeswoman said.
The security breaches came nearly a month after Harambe, a siverback gorilla, was shot and killed by his handlers at the Cincinnati Zoo to protect a 4-year-old boy who had slipped into the pen. The gorilla's death lead to widespread outrage over zoo security and the treatment of animals in captivity.