News agency Reuters quoted Australian police as saying, "The packages are being examined by attending emergency services".
"The circumstances surrounding the incidents are being investigated", the statement said.
Embassies in Canberra have also been targeted.
Seven foreign consulates have been evacuated in Melbourne after the discovery of suspicious packages.
A number of consulates have been evacuated in Melbourne.
A spokesman for the USA consulate in Melbourne also confirmed it had received a suspicious package.
A British High Commission spokesperson also confirmed that a suspicious package was sent to their Melbourne consulate and they were liaising closely with Australian Federal Police and the local authorities regarding the situation.
Switzerland win Hopman Cup
Zverev had a glimmer of hope in the first game of the second set, 0-30, and two deuces, but the Federer serving was just too good. Maria Sakkari could not resist the fan side of her when she was up against Roger Federer at the Hopman Cup.
Two fire trucks, a hazardous materials vehicle and police cars were called to the Consulate-General of India on St Kilda Road, where staff sat outside the building, telling reporters they had been told not to comment to reporters.
The ministry said staff were evacuated as a precautionary measure.
The United Kingdom Consulate, located on Collins Street, along with the Korean Consulate (St Kilda Road), German Consulate (Queen Street), Italian Consulate (St Kilda Road), Swiss Consulate (Ashwood), Pakistan Consulate (Cardigan Place), Greek Consulate (Albert Road) and the Indonesian Consulate(Queens Road) are among locations believed to have been affected.
Images taken by 9News show firefighters and Ambulance Victoria paramedics attending the Indian Consulate and US Consulate on St Kilda Road.
The Swiss consulate in Melbourne was sent a small envelope containing a substance labelled "asbestos", said Peter Erb, the husband of honorary consul Manuela Erb.
"We are assisting at a number of embassies across Melbourne", she said.
Emergency workers wearing chemical suits were seen entering some of the buildings.