Embassies in Canberra have also been targeted.
However the U.S. embassy in Canberra was not targeted with a package, a spokesperson said.
News agency Reuters quoted Australian police as saying, "The packages are being examined by attending emergency services".
A spokesman for the US Consulate in Melbourne also confirmed they had received a package which local authorities are investigating.
Local media reported that emergency workers had been seen at consulates belonging to India, South Korea, New Zealand, Greece and Italy. It was not clear which embassies in Canberra were affected.
Melbourne's Metropolitan Fire Brigade (MFB) has sent vans to reports of "hazardous material" at 16 sites, according to the Vic Emergency website.
The Indian and United States consulates on St Kilda Road as well as the British, Swiss and German diplomatic mission are believed to have been targeted.
It is understood at least seven Melbourne buildings have been evacuated.
"At this time we believe the matter is targeted and not impacting the general community", the statement said.
Emergency services in Australia are responding to multiple reports of suspicious packages delivered to a number of embassies and consulates in Canberra and Melbourne.
Victoria police issued a statement saying it was aware of "a number of consulate offices in Melbourne today receiving suspicious packages".
Hazmat and fire crews work outside the Indian and French Consulate in Melbourne, Australia.
The official said she was told by the authorities to wash her hands.
The journalist also said that Hazmat crews (they deal with unsafe substances) had entered the consulate building. Inside were plastic sandwich bags containing a fibrous material.
There is also a warning listed in Ashwood, where the Swiss consulate is located.