Burglars broke into the building on Victoria state's Mornington Peninsula, south of Melbourne, in what was believed to be a targeted robbery.
"The offender(s) have forced open cabinets inside and stolen numerous priceless antiques," a police statement said.
"The stolen items included a ring and (a glass frame) containing Napoleon's hair, a ribbon inscribed by Napoleon in 1815 and a snuff box."
The thieves removed outside blinds and entered through a bathroom of the historic Briars Park homestead in Mount Martha last Thursday night.
The museum said the collection was put together by descendants of Englishman Alexander Balcombe, who met Napoleon when he was exiled on the tiny South Atlantic island of St Helena from 1815 until the emperor's death six years later.
Balcombe had "sat on Napoleon's knee as a little boy", museum coordinator Steve York told the Australian Broadcasting Corporation.
"The family were good friends with the emperor when he was sent into exile on St Helena," he added.
Balcombe settled in Australia in 1846.
Ten items were taken from the collection, including locks of Napoleon's hair and a silver inkwell set with three gold Napoleon coins which were allegedly in his pocket when he died.
Miniature portraits of Napoleon and Josephine were also stolen.
"Really they're priceless because they can't be replaced. We're quite distraught," York said.
The rest of the collection of nearly 500 pieces has now been re-located for safety.
Police said the robbery appeared to have lasted just 10 minutes and been a targeted theft.
"We think it's probably destined for a private collection. It could well be stolen to order," Detective Sergeant Michael Lamb told the ABC.