Spyros Louis was presented with the cup, a silver medal, an antique vase, an olive branch and a diploma by Greece's King George I for his Athens victory over 25 miles (40 kilometres) — slightly shorter than the modern marathon.
Auction house Christie's says the engraved 6-inch (15-centimetre) cup had been in Louis' family for 116 years but will be sold by his grandson on April 18.
Louis' grandson, also called Spyros, said Thursday he would give proceeds estimated at 120,000-160,000 pounds ($190,000-$250,000) to his children.
"Our family has been very proud to have the honour of looking after this important historical sporting trophy for the last 116 years," Spyros Louis said. "And my grandfather's achievement of winning the first ever marathon at the first modern Olympic Games will remain part of my family's heritage forever.
"However, it is time to look to the future, not the past. I have two children and the most important thing for me is to ensure that they are looked after as well as possible. It is always going to be impossible to split a cup."
Louis' grandfather qualified for the marathon in the inaugural 14-nation Olympics by finishing fifth in a qualifier.
He took the lead a few kilometres from the end after a competitor ahead of him collapsed and was cheered across the line by more than 80,000 spectators at the Panathinaiko Stadium.
Louis was the only Greek athlete to win at the games and was hailed as a national hero.
Also for sale in an auction of 179 items are eight original Olympic torches dating from 1936 to 1996 and 26 original posters advertising Olympic Games between 1908 and 1964.