MOSCOW—Russia’s inflation rate has accelerated to levels last seen in 2002, leaving the central bank with a policy conundrum as the economy slides into a recession.

Hit by a rapid drop in the price of oil, Russia’s chief export, the country faces an economic and financial crisis similar to the one endured in 2009. But unlike six years ago, the country has been cut off from global capital markets because of Western sanctions imposed after Moscow’s annexation of Ukraine’s Crimean peninsula.

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