"Leonardo: Painter at the Court of Milan" opened this month and runs through Feb. 5. It focuses on the artist's formative years as a court artist in the 1480s and 1490s and includes seven paintings never before put on public display.
The London museum told the BBC some of the $25 tickets to the wildly popular show are selling for as much as $618 apiece on eBay and Viagogo.
"We are obviously very disappointed at the resale of these tickets for profit," a museum spokeswoman told the British broadcaster.
"The resale of tickets for the Leonardo da Vinci exhibition is against the terms and conditions of their sale and this information is printed on the tickets. Our Web site clearly states, 'Tickets that have been resold will be canceled without refund and admission will be refused to the bearer.'"