MOSCOW—Russia’s government is considering freezing prices for some “socially important” goods as inflation nears a four-year high, the government newspaper Rossiyskaya Gazeta reported on Thursday.

Russia had been aiming to bring inflation to a post-Soviet low of 5% this year, but the annexation of Ukraine’s region of Crimea ruined the plan. The annexation and the subsequent sanctions imposed by Western countries have put pressure on the ruble, making imports more expensive. The Kremlin’s decision to ban food imports from states...