Australian Federal Police are now examining the packages, which were delivered to consulates on St Kilda Rd and in the CBD.
The ABC reported one New Zealand consulate worker had said the packages in question were envelopes labelled "asbestos". "The circumstances are being investigated", the Australian Federal Police said.
It was not immediately known which countries' diplomatic missions in the national capital, Canberra, were affected.
Police did not identify any of the embassies or consulates involved.
The Victorian Emergency website lists more than 10 "hazardous material" events occurring across Melbourne, which began unfolding from about 1.00pm.
The Foreign and Commonwealth Office (FCO) said Australian Federal Police are "dealing" with a report of a suspicious package at the British Consulate General in Melbourne.
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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Images on social media reportedly showed emergency services in protective clothing entering various consulates in Melbourne.
There were no immediate reports of any of the consulate staff being harmed in the incidents.
"Staff were evacuated from the Consulate as a precautionary measure", a spokesperson said.
Hazmat and fire crews are seen outside the Indian and French Consulates on St Kilda Road in Melbourne.
"We handled the package according to our standard procedures and in close coordination with local authorities ... who are investigating the incident", a spokesman for the U.S. Consulate said.
The Metropolitan Fire Brigade confirmed shortly before 3pm that it was assisting Australian Federal Police at embassies across Melbourne.
A firefighter is seen carrying a hazardous material bag into the South Korean consulate in Melbourne.