The rare pink diamond was snatched from a jewellery store in the northern city of Cairns last weekend by a man who escaped on a bicycle.
Police arrested 29-year-old Matthew Osborne as he attempted to a board a flight to New Zealand from an airport in the southern city of Melbourne.
Senior Sergeant Greg Giles told Australian Broadcasting Corporation that police had yet to recover the cut diamond and suspected the tourist had swallowed it but that the X-rays were inconclusive.
Mr Osborne will be extradited from Melbourne to Cairns and charged with theft, according to reports.
The diamond's owner, Keith Bird, said police told him the man had admitted stealing the diamond and swallowed it as he prepared to board the flight to New Zealand, but that he doubted this claim.
He said Western Australia state police had the suspect's fingerprints recorded for a traffic offence.