The lunch - including sweetbreads, spring lamb and pastries - was served during the liner’s sea trials on April 2 in 1912.
Second Officer Charles Lightoller, the highest ranking surviving officer from the Titanic, owned the menu.
He gave it to his wife as a souvenir as he left from Southampton on April 10 in 1912.
More than 1,500 passengers and crew died when the Titanic struck an iceberg four days later.
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Auctioneer Andrew Aldridge said: “This menu is one of the most important examples of its type in existence today, simply superb a true blue chip item.
“It has a pre-sale estimate of between £80,000 to £100,000 because it ticks so many boxes.
“It is from most famous ship in the world, the first meal served on it and owned by its most senior surviving officer.
“It also has cross-collectable appeal. It will attract high-end Titanic collectors, those interested in food and fine dining and people who just like iconic objects.”
Titanic was due to leave Belfast for Southampton on April 1, but this was postponed until the following day due to bad weather.
Sea trials began at 10am on April 2, with the ship sailing all day and returning to port for some last-minute cargo.
“During this day, the crew and the officers enjoyed their first meal on board the ship before she was joined by the passengers,” Mr Aldridge said.
The ship was put at dead slow while lunch was served in the main dining saloon. After the diners finished, the major stopping test was conducted.
It is believed that only one other example of a menu from April 2 survives.
This belonged to Titanic’s Fifth Officer Harold Lowe, who noted on it: “This is first meal ever served on board”.
Henry Aldridge and Son in Devizes, Wiltshire, sold this menu for £28,000 in 2004 - but the bottom of it was removed.
They will auction Lightoller’s menu on April 21.