Jennifer Foster, of Florence, Ariz., was visiting New York with her boyfriend on Nov. 14, when she came across the shoeless man asking for change in Times Square.
As she was about to approach him, she said the officer - identified as Larry DePrimo - came up to the man with a pair of all-weather boots and thermal socks on the frigid night. She recorded his generosity on her cellphone.
It was posted Tuesday night to the NYPD's official Facebook page and became an instant hit. More than 360,000 users "liked" it as of Thursday afternoon, and over 100,000 shared it.
Thousands of people commented, including one person who praised him as "An officer AND a Gentleman."
The photo shows the officer kneeling beside the man with the boots at his feet. A shoe store is seen in the background.
The NYPD Facebook page on Thursday posted a comment from DePrimo saying, "I didn't think anything of it," and updated it with a photo of DePrimo taken in 2011.
"I have these size 12 boots for you, they are all-weather. Let's put them on and take care of you," Foster quoted DePrimo as saying to the homeless man.
She wrote: "The officer squatted down on the ground and proceeded to put socks and the new boots on this man. The officer expected NOTHING in return and did not know I was watching."
Foster, who is a dispatch manager at the Pinal County Sheriff's Office, said she's worked in law enforcement for 17 years and has never been more impressed.
"His presentation of human kindness has not been lost on myself or any of the Arizona law enforcement officials with whom this story has been shared," Foster wrote on Facebook. She said she never got the officer's name.
DePrimo is assigned to the Sixth Precinct, encompassing Greenwich Village and the West Village, and lives on Long Island. He told Newsday that the homeless man "smiled from ear to ear" after getting the boots.
"It was like you gave him a million dollars," he added.
He told The New York Times that he keeps the receipt for the boots in his vest to remind him "that sometimes people have it worse."