The Bank said Russia, a major oil producer, would be particularly hard hit by the low price of oil.
It said the Kremlin should shift the focus of its anti-crisis programme to the poor because of "the threat of significant social pressure".
The Bank added that aid to Russia's poor might have the added benefit of stimulating domestic demand.
Unrest feared
The World Bank says that the social situation in Russia has worsened so rapidly and so unexpectedly that it is important to shift the focus of the anti-crisis policy to the population.
It says that the Russian government should increase payments to the unemployed and to pensioners.
Since the global economic downturn began to affect Russia, the authorities here have been worried by the prospect of social unrest - especially in towns where single enterprises are the engine of the entire local economy.
The government insists that it has the funds to meet social spending requirements, but the World Bank's prediction is likely to cause further concern.
While the Bank expects the Russian economy to shrink by 4.5% this year, the Russian government predicts a 2.2% contraction.
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