The watchdog, Roskomnadzor, said in a statement on its website that it had sent telecoms operators a notification about blocking access to Telegram inside Russia.
The service, set up by a Russian entrepreneur, has more than 200 million global users and is ranked as the world's ninth most popular mobile messaging app.
A Roskomnadzor official said it would take several hours to complete the operation to block access, Interfax news agency said.
In Moscow, the Telegram app was still functioning as normal by mid-afternoon on Monday, but the company's website had been blocked by two of Russia's biggest service providers, MTS and Megafon .
Both MTS and Megafon declined to comment.
Roskomnadzor was implementing a decision handed down on Friday by a Russian court, which ruled that Telegram should be blocked because it was in violation of Russian regulations.
Telegram has repeatedly refused to comply with requests to give Russia's Federal Security Service (FSB) access to its users' encrypted messages.