Armstrong's fellow lunar pioneers, Buzz Aldrin and Michael Collins, each received one as well.
These are the only three known to be in existence.
The museum closed its doors on Saturday and said in a statement on Facebook: "The truth is that you can't steal from a museum. Museum's don't "own" artifacts.
"We are simply vessels of the public trust. Museums care for and exhibit items on behalf of you, the public. Theft from a museum is a theft from all of us."
The local police department are continuing with their investigation with help from the FBI.
10 incredible auctions
10 incredible auctions
The most expensive watch ever sold at auction fetched just under $24 million in November 2014. The gold pocket watch was made by Patek Philippe, and is the most complex ever made without the use of computer technology.
The Henry Graves Supercomplication was commissioned in 1925, and took eight years to make.
The world's most expensive stamp sold at auction in 2014 for over $9 million.
The British Guiana One-Cent Magenta is as rare as a stamp can get. British Guiana was one of the first countries in the New World to start issuing stamps, but in 1856, they ran out, and asked the local newspaper printer to produce extras.
There were two denominations: the four-cent, which is very rare, and the one-cent - of which only one has ever been discovered.
In May 2015, an anonymous London businesswoman snapped up the licence plate KR15 HNA for £233,000, making it the most expensive standard number plate ever to be sold in the UK.
Queen Victoria's bloomers sold at auction for £6,200, along with a pair of her silk stockings.
They have a 52-inch waist, and belonged to the monarch in the 1890s - "towards the end of her life when she had eaten a lot more than most people could afford to," said auctioneer Michael Hogben. In today's sizing, they'd be a size 26.
In 2014, a three-year-old slice of cake sold at auction for $7,500 (£4,800). The reason the stale cake was in such demand was that it was from the marriage of Prince William to Kate Middleton in 2011.
The buyer said he intended to give it away as part of promoting his Silicon Valley start-up.
A British coin sold at auction for a record-breaking £430,000 in 2014. After fees, the buyer paid £516,000 - making it the most expensive modern British coin ever to be sold.
The coin is only one of two in existence. It was a 'proof' for a gold sovereign which was meant to be produced to commemorate the coronation of Edward VIII in 1937. However, Edward abdicated in 1936, so the coronation never happened and the coins were never made