Prime Minister Anthony Albanese said intelligence agencies had given "very clear security advice" on the move.
Laws specifically drafted to halt construction were rapidly passed on Thursday after legal attempts to block the Canberra development failed.
The Kremlin said it was "yet another unfriendly action" which Russia would "take into account" in the future.
Australia was following the "Russophobic hysteria that is now going on in the countries of the collective West", said spokesman Dmitry Peskov.
A Russian diplomat earlier told AFP that the embassy was seeking legal advice.
The new legislation acknowledges that Russia may be eligible for financial compensation.
The current embassy will not be affected by the new laws, which have bipartisan support.
Moscow currently holds the lease for a patch of land, acquired in 2008, some 400 metres (0.25 miles) from Canberra's Parliament House.
It has been laying the foundations for a new embassy building, but construction has proceeded slowly.
As relations between Australia and Russia soured in the wake of the invasion of Ukraine, the former moved to rescind permission for the new building.
A previous attempt to cancel the lease was thrown out by the federal court last month, prompting the new legislation.
The laws took less than five minutes to be introduced, and passed through the House of Representatives.
"We don't expect Russia is in a position to talk about international law, given their rejection of it so consistently and so brazenly with their invasion of Ukraine," said Mr Albanese, who condemned Russia's "illegal and immoral" invasion of Ukraine.
Former UK diplomat Alex Bristow of the Australian Strategic Policy Institute, told AFP that Russia has some of the "largest, most capable, most aggressive, and least constrained intelligence services" in the world.
"Given the proximity, it could be a form of electronic surveillance operating out of the embassy," he added.