Watchdog Rospotrebnadzor claimed the restaurants had breached “numerous” sanitary laws.
McDonald’s said it was looking at the complaints, adding its “top priority is to provide safe and quality products”.
The closures come amid rising tensions between Russia and the West over the crisis in the Ukraine.
Previously when diplomatic tensions are high, the regulator has controversially banned products including wine from Georgia, cheese from Ukraine and apples from Poland.
Earlier this month, Russia imposed a “full embargo” on food imports from the EU, US and some other Western countries, in response to sanctions over Ukraine.
Wednesday’s action by the regulator is part of an ongoing investigation into McDonald’s food standards in Russia.
In July the watchdog filed a lawsuit in Moscow urging the restaurant chain to withdraw certain products.
McDonald’s said that restaurants on Pushkin Square, Manezh Square and Prospect Mira in Moscow had been temporarily closed, and said it wanted to “re-open the restaurants as soon as possible”.
“We will continue taking care of our employees and will do our best to continue the success of McDonald’s business in Russia,” the company added.
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