The bungle happened just before midnight on Friday, according to the New York Police Department.
But, police later found the ring and are looking to find its owners.
The couple then left the area.
Miraculously, the ring was eventually recovered by ESU members who returned to the scene Saturday morning.
The police say that the man stands at around 5ft8in and weighs between 150 and 160 pounds.
The woman is blond, and the man is brown-haired and bearded and wearing a gray cap.
The female is a 5ft5in blonde.
"WANTED for dropping his fiancée's ring in @TimesSquareNYC", the New York Police Department tweeted on Saturday.
NYPD Commissioner James O'Neill used his own Twitter feed in hopes of locating the couple.
He was so excited when she said yes he promptly dropped the ring down a grate underfoot.
Officers also shared a picture of the newly cleaned gleaming ring, asking people to get in touch "if you know the happy couple so we can return it to them!"