For most countries, the economic slowdown in China and the accompanying slump in commodity prices represent something between nuisance and pothole. For Russia, they are a catastrophe.

Russia’s currency and economy, already squeezed by Western sanctions, have been sent into virtual free fall by slumping oil prices. The International Monetary Fund predicted in July that Russia’s economy would shrink 3.4% this year, the most of any major emerging market.

That...