It also ordered them to delete all of Vashukevich's online videos and pictures showing Deripaska, the spokeswoman Oksana Shareiko told AFP.
Aluminium tycoon Deripaska had sought two million rubles in damages. He had accused Vashukevich of violating his privacy.
He sued the self-styled model Vashukevich and Kirillov over a video she apparently shot on his yacht.
It appeared to show Sergei Prikhodko, an influential Russian deputy prime minister at the time, vacationing on Deripaska's yacht.
Prikhodko had formerly been President Vladimir Putin's foreign policy advisor.
The video raised new questions about Russia's alleged meddling in the 2016 presidential election that brought Trump to power.
Deripaska was once an associate of Trump's former campaign director Paul Manafort.
Russian opposition figure Alexei Navalny published the video in an investigation into corruption among top government officials.
In a rare statement to the press, Prikhodko called Deripaska "my friend" and added that he did not know Manafort personally.
The state media watchdog earlier this year threatened to block Instagram and YouTube if the two sites did not delete the videos and pictures of Deripaska and Prikhodko.
Vashukevich is a national of ex-Soviet Belarus. She goes by the nickname Nastya Rybka.
She, Kirillov and several others were detained in Thailand in February when police raided their "sex training course" in the seaside city of Pattaya.
The two defendants were not present at the Russian ruling on Monday. They are still awaiting trial in Thailand.
A pre-trial hearing in Pattaya is scheduled for July 19.
In Thailand, the model has made cryptic offers to reveal secrets about alleged Russian meddling in the 2016 US election. (See story here.)
She has penned a book about how to seduce an oligarch.
She has 130,000 followers on Instagram where she has posted snaps of herself scantily-clad or naked and a video of her apparently having sex with a man.