It was given to former Prime Minister Willem Drees during a goodwill tour by the three Apollo-11 astronauts shortly after their moon mission in 1969.
When Mr Drees died, the rock went on display at the Amsterdam museum.
At one point it was insured for around $500,000 (?308,000), but tests have proved it was not the genuine article.
The Rijksmuseum, which is perhaps better known for paintings by artists such as Rembrandt, says it will keep the piece as a curiosity.
"It's a good story, with some questions that are still unanswered," Xandra van Gelder, who oversaw the investigation that proved the piece was a fake, was quoted as saying by the Associated Press news agency.
"We can laugh about it."
The "rock" had originally been been vetted through a phone call to Nasa, she added.
The US agency gave moon rocks to more than 100 countries following lunar missions in the 1970s.
US officials said they had no explanation for the Dutch discovery.
