Russian internet watchdog Roskomnadzor has restricted access to the websites of Open Media and MBKh Media, as well as the website of the Pravozashchita Otkrytki human rights group following a request from prosecutors, they said.
Both the rights group and Open Media said on Thursday they were shutting down to shield staff from possible prosecution.
In a statement on Twitter, Open Media, which was founded in 2017 with Khodorkovsky's financial backing, said that Russian authorities did not want critical media. "But at least we tried," it said.
A number of independent media organisations and groups have been banned in Russia in recent months as part of an increasing crackdown on the opposition ahead of parliamentary elections in September
Open Russia, an opposition group founded Khodorkovsky, was designated an "undesirable" organisation in Russia in 2017 in line with a law targeting foreign groups accused of political meddling. In May, the group said it was closing to protect its members from prosecution.
Khodorkovsky, who owned the oil giant Yukos before he was convicted in two controversial cases and spent a decade behind bars, now lives abroad.
In July, authorities outlawed Proekt, one of the country's last independent media outlets that focused on in-depth reporting into the wealth of Russia's elite including President Vladimir Putin.
The same month the media regulator blocked 49 websites linked to jailed Kremlin critic Alexei Navalny including his main website navalny.com.
Russia's parliamentary vote will be held from September 17 to September 19.
On Wednesday, international monitors said they would not send observers to Russia for the September election because of a limit on numbers imposed by Russian authorities.
