The newspaper said it would continue to report on the consequences that Russia is facing, including a deepening economic crisis and the persecution of dissidents.
"Military censorship in Russia has quickly moved into a new phase: from the threat of blocking and closing publications (almost fully implemented) it has moved to the threat of criminal prosecution of both journalists and citizens who spread information about military hostilities that is different from the press releases of the Ministry of Defence," the paper said in a message to readers.
"There is no doubt that this threat will be realised."
The newspaper said it could not risk the freedom of its staff but also could not ignore its readers' desire for it to continuing working, even under military censorship.
It said it was therefore removing materials "on this topic" from its website and social networks.
"We continue to report on the consequences that Russia is facing: the developing economic crisis, the rapid decline in living standards, problems with access to foreign medicines and technologies and the persecution of dissidents, including for anti-war statements," it said.
Muratov, the editor, dedicated his Nobel prize last year to six of the newspaper's journalists who had been murdered for their work.
On the day of Russia's invasion of Ukraine last week, he told the BBC: "Our peace-loving Russian people will now feel the hatred of the world because we are starting a third world war in the centre of Europe."
Novaya Gazeta's announcement followed the closure this week of radio station Ekho Moskvy, another of the few remaining independent voices in the Russian media.
Refusing to give up its editorial independence, Ekho Moskvy's board of directors voted to close the station after the prosecutor general's office demanded restrictions on access to it because of what it called false reporting on Russia's "special military operation" in Ukraine.Â
