The government Vic Emergency website noted at least 10 "hazardous material" incidents in the city. There were no reports of anyone being injured at the targeted missions in both cities.
"The circumstances surrounding these incidents are being investigated," the Australian Federal Police said in a statement.
The Australian Broadcasting Corp. reported that a worker from the New Zealand consulate in Melbourne had said the packages in question were envelopes labelled "asbestos." Inside were plastic sandwich bags containing a fibrous material.
The ABC reported suspicious packages were also found at the Melbourne diplomatic offices of Pakistan and possibly those of Greece, France and Hong Kong. It said the Israeli Embassy in Canberra also received a suspicious package.