Burglars broke into The Briars historic homestead, in Mount Martha, south of Melbourne, through a bathroom window last Thursday, police said.
The stolen items include a ring, a tuft of Napoleon's hair, a ribbon inscribed by him in 1815 and a snuff box.
"Really they're priceless because they can't be replaced. We're quite distraught. Irreplaceable," Museum coordinator Steve York told the Australian Broadcasting Corporation.
Some miniature portraits of Napoleon and Josephine were also taken.
The rest of the collection has been relocated.
The collection of artefacts was put together by Dame Mable Brooks who was the great-granddaughter of Alexander Balcombe, who met Napoleon in exile on St Helena Island.