By Agence France-Presse
The plaque includes a representation of the lunar module that touched down on the moon on July 20, 1969.
Once back on Earth, it was mounted on a wooden base before being offered to Armstrong, the first man to set foot on the Moon.
The other two astronauts who took part in the mission, Edwin "Buzz" Aldrin and Michael Collins, also each received one of these plaques.
Armstrong's two sons, Rick and Mark, decided to part with some of the very large collection of their father, who died in 2012. It includes more than 2,000 objects.
Just part of the collection was offered at the sale held Thursday through Saturday in Dallas as well as online.
Another two sales are planned in May and November 2019 by Heritage Auction, which organized the first.
The souvenir plaque did better than the lot that was expected as the highlight of the sale, an American flag taken during the trip to the moon, but never deployed on site.
Larger than most flags brought into space (45 by 29 centimeters, or 18 by 11 inches), it was sold for $275,000, including fees and commissions.
That's more than triple Heritage's estimate of $75,000.
Among Armstrong's collection were two batches of fragments of the Wright brothers' plane, whose first flight, in December 1903, is considered modern aviation's maiden voyage.
These pieces were taken by Armstrong on the Apollo 11 mission and thus have a double historical value. They each sold for $275,000, or nine times the original estimate.
In all, the first part of the Armstrong collection selloff has earned $5.2 million, Heritage Auctions said in a statement.