"For us and, I know, for you, this is a terrible and difficult decision. But we need to save us for each other," he said in a statement. The announcement came more than a month into the Kremlin's military campaign in pro-Western Ukraine.
"We have received another warning from Roskomnadzor," the newspaper said in a statement, referring to Russia's media regulator.
"We are suspending publication of the newspaper on our website, on social media and in print -- until the end of the 'special operation in Ukraine'," it added.
Co-founded by former Soviet leader Mikhail Gorbachev in 1993, Novaya Gazeta is the only main newspaper left voicing criticism of President Vladimir Putin and his tactics in and outside the country.
Earlier on Monday, Novaya Gazeta staff learnt of a formal warning from Roskomnadzor state communications watchdog, its second since last week.
Nadezhda Prusenkova, a Novaya Gazeta spokeswoman, told AFP that the newspaper still did not have a copy of the warning, adding they had learnt about the development "from the news."
If a media outlet receives two warnings from the communications regulator in the space of a year, a court can shut it down.
Last week, Roskomnadzor said Novaya Gazeta failed to mark a non-governmental organisation mentioned in one of its stories as a "foreign agent" in accordance with Russian legislation.
Russia is seeing an unprecedented crackdown on dissenting voices and independent journalism that has included dubbing non-governmental organisations and media outlets as "foreign agents" -- a label that carries strong pejorative connotations and implies an increased government scrutiny.
Novaya Gazeta itself has not been declared a "foreign agent". Last year, Muratov was awarded the Nobel Peace prize alongside Maria Ressa of the Philippines for their efforts "to safeguard freedom of expression".
Last week, Muratov said the newspaper had decided to donate the gold medal to a fund to help Ukrainian refugees.