The country has also been subject to economic sanctions by the West over its involvement in the crisis in Ukraine.
Russia will spend most of the cash on federal loans, pensions and recapitalising its banks.
The country will also make public spending cuts.
Over the next three years most spending, apart military and social programmes, will be hit.
Earlier this month, the International Monetary Fund forecast that Russia's economy will contract by 3% this year and 1% in 2016.
Russia's government will spend about one trillion roubles to recapitalise banks through the issue of government bonds.
The plan includes a separate scheme to help recapitalise some banks with 250bn roubles, while 300bn roubles will be provided to Vnesheconombank, the state development bank.
There will be an extra 200bn roubles in state guarantees to finance investment projects, and regional governments will get 160bn roubles in federal loans.
Meanwhile, the government has proposed public spending cuts of 10% this year and 5% over the next two years.
The cuts have yet to be approved by the Russian parliament.
The Russian government is to spend at least 2.34 trillion roubles ($35bn, Â£23bn) to try to stave off an economic crisis, following a collapse in oil prices and the value of the rouble.