The AFP said some embassies and consulates in Canberra had also been affected.
An AFP spokesperson said that as the matter is subject to further inquiries, they would not be providing further information.
Emergency service personel exit the building where the Korean consulate is located in Melbourne.
"We are aware of reports of suspicious packages being received and are cooperating with the AFP", a British consulate spokesman said.
The city's Metropolitan Fire Brigade sent units to "a number of incidents" of "hazardous material".
"The circumstances surrounding the incidents are being investigated", said the Australian Federal Police.
SYDNEY: Pakistan's mission in Melbourne was among the those global consulates and embassies in Australian cities that have been sent suspicious packages containing white powder, some reportedly marked with the word "asbestos", foreign media reported.
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Images taken by 9News showed firefighters and paramedics attending the Indian and USA missions in Melbourne.
All of the incidents that matched the addresses of consulates in Melbourne were declared under control.
The Vic Emergency website lists more than 10 "hazardous material" events occurring across Melbourne, which began unfolding from about 1pm.
The New Zealand consulate in Melbourne, Australia was sent a suspicious package, MFAT has confirmed.
"It's believed to be non-hazardous, however, they're treating it as a hazardous", she said.
The packages were not believed to be unsafe, but police, fire crews and forensic teams were urged to use breathing apparatus as they documented and double- or triple-bagged the materials for further testing.
According to the ABC, a New Zealand consulate worker told the press that the package had been labeled "asbestos" and contained several plastic bags holding fibrous material.