It lists the dinner - including oysters, beef, spring lamb and mallard duck - served on the evening of 11 April 1912.
More than 1,500 people died when the Titanic struck an iceberg in the Atlantic Ocean on 14 April 1912, causing the boat to sink.
The sale on Saturday was run by Henry Aldridge & Son in Devizes, Wiltshire.
Auctioneer Andrew Aldridge said: "The menu is a remarkable survivor from the most famous ocean liner of all time."
The menu bears an embossed White Star Line flag and would have originally shown gilt lettering depicting the initials OSNC (Ocean Steamship Navigation Company) alongside the lettering "RMS Titanic".
Mr Aldridge said the menu showed signs of water immersion as the text was partially erased.
"This would point to the menu having been subjected to the icy North Atlantic waters on the morning of April 15 either having left the ship with a survivor who was exposed to those cold sea waters or recovered on the person of one of those lost.
"Having spoken to the leading collectors of Titanic memorabilia globally and consulted with numerous museums with Titanic collections, we can find no other surviving examples of a first-class April 11 dinner menu."
Other items in the auction included a Swiss-made pocket watch, owned by second-class Titanic passenger, Sinai Kantor. It sold for Â£97,000.
A first-class tartan-patterned deck blanket, which may have been used during the rescue of passengers also sold for Â£96,000.
The auctioneer is well-known for selling memorabilia from the doomed passenger ship.
A fur coat owned by a first-class stewardess sold by them for Â£150,000 in 2017.
In the same year,a letter by Titanic passenger Oscar Holverson soldfor Â£126,000.
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An evening dinner menu for first-class passengers onboard the RMS Titanic has sold for Â£84,000 at auction.