It shows Andrew peering out from a large door of the mansion waving goodbye to a woman after Epstein leaves to get in a chauffeur-driven vehicle.
Epstein, who was found dead in his jail cell earlier this month, was accused of arranging to have sex with dozens of underage girls at his residences in NY and Florida.
The footage is believed to have been filmed in December 2010, two years after Mr Epstein pleaded guilty to charges of soliciting prostitution from girls as young as 14.
Video obtained by the Mail Online apparently shows the Duke of York peering out from a door of Epstein's NY mansion and waving goodbye to a woman after Epstein had left an hour earlier in the company of another young woman. "His Royal Highness deplores the exploitation of any human being and the suggestion he would condone, participate in or encourage any such behaviour is abhorrent", according to the statement released on Sunday.
Jeffrey Epstein died in jail earlier this month.
Epstein first came under investigation in 2005 after police in Palm Beach, Fla., received reports he had sexually abused underage girls in his mansion there.
The video was the latest in a string of revelations about Prince Andrew's friendship with Epstein in British tabloids.
Andrew's connections to Epstein came under fresh scrutiny following newly unsealed legal documents on August 9.
A mutual friend of both men told Vanity Fair they phoned the prince after Epstein's conviction in 2011 but was rebuffed and told by Andrew: 'Being loyal to your friends is a virtue.
The duke quits his role as United Kingdom trade envoy after fallout from the the Central Park photos. But the palace has repeatedly issued statements denying any wrongdoing by Andrew.
The disturbing allegations resurfaced in light of Epstein's apparent suicide in his Metropolitan Correction Center jail cell last week.
Virginia Roberts claimed she was forced to have sex with the prince on three occasions - in London, New York and on a private Caribbean island owned by Epstein - between 1999 and 2002, when she was under-age according to USA law.