"The circumstances are being investigated", the Australian Federal Police said.
Some reports said as many as 22 consulates had received packages, some of which apparently contained asbestos.
"All our staff are safe and accounted for".
"The packages are being examined by attending emergency services", the Australian Federal Police (AFP) said in a short statement.
Emergency services were first alerted to the packages in the Melbourne locations about 12.30pm.
The discovery of suspicious substances at the Argentinian consulate in Sydney prompted a large scale emergency response just two days ago.
The Ministry of Foreign Affairs and Trade has confirmed that the New Zealand Consulate General in Melbourne received a suspicious package this afternoon.
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"At this time we believe the matter is targeted and not impacting the general community", said the spokesperson.
Melbourne emergency services have responded to a number of call-outs for "hazardous material" in the last hour according to the state's emergency response website, which shows a total of 17 hazardous material incidents now in progress.
Emergency Management Victoria maps showed 11 active hazardous material incidents on Wednesday afternoon, but the number was rapidly falling.
"We handled the package according to our standard procedures and in close coordination with local authorities - the Melbourne Fire Brigade, the Victoria Police, and the Australian Federal Police - who are investigating the incident".
Officials at the US and British consulates separately confirmed suspicious packages had been received. It was not clear which embassies in Canberra were affected.
"It's believed to be non-hazardous, however they're treating it as hazardous", she said.
The NZ consulate was one of at least seven global consulates evacuated after multiple suspicious packages were found, in what officials labelled a "hazardous material" event.