Emergency services attended consulates across Melbourne's central busy district and the inner city.
The statement Wednesday said: "The circumstances surrounding these incidents are being investigated".
Victoria Police said there was no threat to the public: "At this time we believe the matter is targeted and not impacting the general community".
They include United States, Britain, New Zealand, India, Japan, Pakistan, Korea, Germany, Greece, Spain, Seychelles, Switzerland, Croatia and Egypt.
The Swiss consulate in Melbourne confirmed to CNN that a suspicious package was delivered at around 1.30 p.m. local time Wednesday (9.30 p.m. Tuesday ET), and that the police and fire services are now investigating.
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There was also an alert of a hazardous material incident at Yertchuch Avenue in Ashwood, in Melbourne's eastern suburbs, where the Swiss consulate is based.
The NZ consulate was one of at least seven worldwide consulates evacuated after multiple suspicious packages were found, in what officials labelled a "hazardous material" event.
"It's believed to be non-hazardous, however, they're treating it as a hazardous", she said.
Some unverified reports claimed that the diplomatic missions have received packages bearing the word "asbestos" and "wear a mask". Metropolitan Fire Brigade and Ambulance Victoria are investigating.
The Indian High Commission is located in Canberra; there were no immediate reports of the high commission being among the locations that received suspicious packages.
Sky reported that the scare coincided with the USA embassy's hazmat training, which had been booked for months.
Paramedics and firefighters wearing hazmat suits were seen entering the Korean embassy, while fire engines were seen outside several consulates.