Sources told the Reuters news agency over the weekend that the government wants to sell minority stakes in firms such as Rosneft, Russia's biggest oil producer; VTB, a lending company; and Transneft, the Russian oil pipeline monopoly.
Kudrin sought to ease investor fears about transparency, insisting that the assets would be sold on the open market.
"We will sell significant stakes in state companies on the market. We plan to keep controlling stakes," he said.
"[Assets] will be valued publicly, in line with market prices and tenders will be open.
"We are fully ruling out a situation when somebody sells something to someone at an artificially low price."
The sale would be Russia's most ambitious since Boris Yeltsin was president, when well-connected tycoons snapped up some of the biggest oil and metals firms at low prices.
Investors have applauded the new plan, which would see Russia still control the firms, but it remains unclear whether transparency will be ensured and whether foreigners will be allowed to bid.
The plan could help the Kremlin plug holes in the state finances, with Kudrin saying that Russia was unlikely to be able to balance its budget deficit until 2015.
Vladimir Putin, the Russian prime minister, has said the country may not be able to reduce the deficit below five per cent - or $80bn - this year.
The government is likely to want to maintain high social spending to boost its electoral chances in the presidential polls in 2012 and the planned sell-off could avoid the need for to increase taxes.