The woman, travelling through the country's busiest airport on Tuesday, was given the unclaimed bag as a replacement after her one was damaged during a flight.
When she reached home and opened the suitcase, she found 230 grams of plastic explosive in a training device and took it to a local police station in Cessnock, about 150 kilometres from Sydney.
Officers evacuated the building as a precaution and traced the explosives back to the Australian Federal Police.
Police said the device was not live and was inadvertently left at the domestic terminal after a detector dog training exercise on August 14.
"Police takes this error seriously and the canine instructor who inadvertently left this device behind has been identified and will be the subject of a formal professional standards investigation," federal police Sydney airport Commander Wayne Buchhorn said.
"Although the travelling public was not in danger at any time, we regularly review our processes in this area, and we will do again in the light of this incident."
Police dogs are a routine sight at Sydney airport, sniffing passengers, bags, vehicles and the terminal buildings for illegal drugs, explosives and currency.
"This type of training is essential for our canine teams, allowing the dogs to experience potential threats in a real environment," police added.
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"the canine instructor who inadvertently left this device behind has been identified and will be the subject of a formal professional standards investigation"
That's the ticket... Mistakes happen in Western countries, but these are acknowledged, fixed and preventive action is taken. Unlike in our countries, where things are swept under the carpet (by appointing committees), or blame is passed to someone else or conspiracy theories are evoked.
If this had happened in Pakistan it would have been labelled as a deliberate terrorist threat.