The Armstrong Air and Space Museum was broken into late Friday night. The thief or thieves made it out of the building with an 18-karat gold Apollo 11 lunar module replica.
The piece was made by Cartier and was gifted to Armstrong by the French paper, La Figaro, not long after the moon landing.
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.