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.
