The painting by 17th century artist Charles Le Brun (1619-1690) had adorned one of the suites in which fashion designer Coco Chanel lived for more than 30 years.
Its presence came as news to hotel management when it was discovered in July 2012, a month before the Ritz closed its doors for a two-year renovation.
"The Met does not yet have a work by Charles Le Brun (so) this completes its collection of 17th century paintings," said Lefeuvre, adding that the work was sold at auction on Monday.
The painting is expected to go on display in New York from the end of May.
Proceeds from the sale will go to the foundation established by Ritz owner Mohamed Al Fayed in memory of his son Dodi, the late boyfriend of Princess
The oil painting has been identified by experts as an early work by Le Brun that would have been completed before he became the official painter at the court of Louis XIV, and established his reputation as one of the dominant figures of 17th century French art.
The building that houses the hotel on the swanky Place Vendome dates from 1705 and was initially a family home for French nobles. It became the Ritz after it was bought by Swiss hotelier Cesar Ritz in 1898.
The painting depicts the killing of Trojan princess Polyxena after she was implicated in the death of Achilles. In the absence of any historical records, Christie's have named the painting 'The Sacrifice of Polyxena'.