The journalist had won the prestigious award in 2021, alongside Filipino journalist Maria Ressa - the committee honoring them "for their efforts to preserve freedom of expression".
The Novaya Gazeta newspaper announced at the end of March that it was suspending its online and paper publications in Russia until the end of the intervention in Ukraine, in the midst of the Kremlin's hardening against dissonant voices.
The auction house Heritage Auctions has been in charge of the sale of the Nobel Prize medal which concludes in Manhattan on Monday evening.
In the morning, the highest bid was $550,000.
Proceeds will go to Unicef's humanitarian program for Ukrainian children displaced by war.
Dmitry Muratov was part of a group of journalists who founded Novaya Gazeta in 1993 after the fall of the Soviet Union.
Before the suspension of its operations, the newspaper was the last to voice criticism of Russian President Vladimir Putin.
Novaya Gazeta is particularly known for its investigations into corruption and human rights abuses in Chechnya.
This commitment has cost the lives of six of his collaborators since the 1990s, including the famous journalist Anna Politkovskaïa, assassinated in 2006. Dmitry Muratov dedicated his Nobel Prize to their memory.
"This newspaper is dangerous for people's lives," he told AFP in 2021.
In a video posted by Heritage Auctions, the journalist says that winning the Nobel Prize "gives you an opportunity to be heard".
"The most important message today is that people understand that a conflict is happening and that we must help the people who are suffering the most," he added, pointing in particular to "children in refugee families.
In early April, Dmitry Muratov was attacked on a train in Russia by an unknown person who sprayed him with a red mixture of oil paint and acetone, causing burns to his eyes.
© 2022 AFP