The Moon rock, weighing about 5.5kg (12lb), was found last year in a remote area of Mauritania.
It is thought to have plunged to Earth thousands of years ago.
Its large size and composition are very unusual. It could fetch around $500,000 (£380,000) when it goes on sale at RR Auction.
It is “one of the most important meteorites available for acquisition anywhere in the world today”, the firm said.
It is made up of six fragments, with the largest piece weighing about 3kg, and displays “partial fusion crust”, a coating created by the heat that sears the rock as it goes through the atmosphere.
Most lunar meteorites found are normally smaller – the size of a walnut or golf ball, said Geoff Notkin, CEO of Aerolite Meteorites, which is selling the rock.
“As soon as we saw this, we knew it was extraordinarily unusual,” he told the Associated Press (AP). “This is close to a once in a lifetime find.”
A natural history museum may be the obvious buyer for such an item but RR says private collectors may see this as a unique opportunity to own a piece of the Moon.
“This is the only way a private collector can get their hands on a piece of the Moon, because the Moon rocks brought back by astronauts are US government property,” Robert Livingston, RR’s executive vice-president, told AP.
The online auction runs until 18 October.