They called emergency services, who eventually found it - but only after the couple had left without giving their names or contact information.
New York Police have found themselves at the centre of a real-life romantic comedy.
It fell about 2.4 metres, police said.
"The unidentified man is described as 5'8" or 5'9" with short brown hair and a beard.
Investigators say crashed Lion Air jetliner 'not airworthy'
Budget airline Lion Air has in recent years risen to become a major player in South East Asia's low cost aviation sector. Investigators initially suggested the aircraft which crashed had an issue with its angle of attack (AOA) sensors.
Police later managed to retrieve the ring and clean it and the hapless couple gave up searching for it.
"WANTED for dropping his fiancée's ring in @TimesSquareNYC!"
Unfortunately for the couple, the NYPD does not have the couple's details, therefore it can't reunite them with the ring.
They also released a picture of the dropped jewellery, saying: "We have your ring!".
More than 350,000 people visit Times Square in midtown Manhattan, known as "The Crossroads of the World", every day.