The boy's mother, Kelly Yi, said they attended the dinosaur exhibit in the summer of 2013. They paid $16 for tickets to the exhibit and were promised a free gift.
Each family member received a pressed penny imprinted with the words "Dinosaur Safari," the New York Post reported.
An employee handed the coin directly to Yi's 3-year-old son, Ethan, the Bronx Supreme Court lawsuit said. Ethan put the penny in his mouth and began choking, the suit said..
"I thought he'd die," Kelly Yi said.
Ethan's parents were unable to dislodge the coin, and took him to an emergency medical clinic. X-rays indicated the coin had entered his stomach.
Doctors said the penny would likely move down his digestive system and come out a few days later, but a subsequent X-ray showed that the penny hadn't moved.
Ethan then underwent an endoscopy and a doctor removed the penny.
The jagged edge of the penny cut the inside of Ethan's stomach, the suit said, and the family received more than $50,000 in medical bills.
The suit seeks unspecified damages from the zoo and the Wildlife Conservation Society.
"I feel really angry and frustrated at the Bronx Zoo," she said. "It's a place where kids play, I thought it was good for kids but it wasn't."