Chris Cooper, the man who recorded the encounter, said the woman called police on him after he asked her to put her dog on a leash.
They were in a part of the park called the Ramble, where dogs are supposed to be on a leash, and Cooper said the dog was running loose and tearing through plants.
"I said to the young woman I said, 'Dogs in the ramble have to be on their leash at all times,'" Cooper said.
That's when he said he used treats to try and lure the dog away from some plant beds just before he began recording.
When the woman began to argue with him, Cooper started to record her on his phone, and that's when she called police.
"They don't like it when you feed their dog treats. And she didn't like that at all. And she immediately grabbed the dog as you can see from the video and started hauling it around by its collar," Cooper said.
The woman, who is white, called 911 and reported "an African American man" was threatening both her and her dog.
"At some point she decided to make it a racial thing and at that point, I guess my thinking was: I can sort of capitulate to this racial intimidation or I can just do what I'm doing and continue recording and document what's going on here. And that's what I did," Cooper said.
The woman eventually put her dog on a leash.
By the time officers arrived at the scene, both she and Cooper had left.
The NYPD confirmed that officers did respond to a reported assault, but said there were no arrests or summons issued for what they described as a "verbal dispute."
Speaking to a local New York station, the woman in the video apologized to Cooper, saying, "It was unacceptable and I humbly and fully apologize to everyone who's seen that video, everyone that's been offended...everyone who thinks of me in a lower light and I understand why they do."
She added that she was fearful because she says before the video began, Cooper had been yelling and offering her dog unknown items.
The video of the incident was posted Monday afternoon and quickly took over Twitter's trending topics with more than 130,000 tweets, many calling for the woman to be fired.
The woman's employer Franklin Templeton announced on Twitter Monday evening that she will be placed on administrative leave pending investigation, adding "We take these matters very seriously, and we do not condone racism of any kind."
An animal rescue group said the owner voluntarily surrendered the dog in the video while the matter is being addressed.