The dinner, at the Blue House compound next to a former royal palace, includes a beef rib dish accompanied by a gravy made with an "exquisite, 360-year-old soy sauce", said a spokesman for Seoul's presidential office.
The age implies it was made in 1657, the year the father of the US Declaration of Independence signatory Benjamin Franklin was born.
Fermented food including soy sauce is a staple in South Korean cuisine, with soy sauces made by famous artisans and fermented for decades - or centuries - sold for tens of thousands of dollars per litre.
In one food show in 2012, a group of artisans displayed soy sauce they claimed had been made 450 years ago, with a price tag of 100 million won ($90,000).
Tuesday's menu also includes a grilled sole - known to be Trump's favourite fish - and an unnamed official told the South's Yonhap news agency: "The menu contains food that has local, traditional flavour that could also appeal to the taste of the US head of state."
Within hours of Trump's arrival in Tokyo, Trump and Abe sat down to cheeseburgers, accompanied by tomato ketchup, and the centrepiece of the state banquet there was a steak.
The Seoul meal also features a prawn that Moon's office said was caught near a disputed island claimed both by the South and Japan.
The Seoul-controlled island off the east coast - called Dokdo in Korea and Takeshima in Japan - is at the heart of a decades-long territorial dispute and diplomatic row between the two countries. Click for more trending news