Two "pieces of eight" have been taken from Mull Museum in Tobermory, along with a foot-long barnacle encrusted scabbard.
The coins, one from Spain and one from Bolivia, came from the San Juan De Sicilia which blew up in the bay in 1588.
The thief managed to open the locked display case which held the items, police said.
Mull police said the crime was "really unusual" and although the items could not be replaced, they had only historical value.
A spokeswoman for Mull Museum said: "We are very sad to lose a unique piece of the history of Tobermory."