The Russian offshoot of the loose-knit movement known as Anonymous tweeted that it had taken down the website of the Khamovniki district court.
Latest song on the website
According to search engines' cached pages, the hackers posted Pussy Riot's latest song ridiculing President Vladimir Putin on the website, along with calls to release the band members. One headline read: "Putin's thieving gang is robbing our country! Wake up, comrades!"
The website — hamovnichesky.msk.sudrf.ru — was not available later Tuesday.
Court spokeswoman Darya Lyakh said the Supreme Court would demand the hackers face criminal charges.
The three female band members were punished for a provocative stunt in February at Moscow's main cathedral in which they asked the Virgin Mary to deliver Russia from Putin, who was elected to a third term two weeks later.
Their trial caused an international furor, and small but raucous protests were held around the world Friday when the women were convicted and sentenced. Celebrities including Paul McCartney, Madonna and Bjork have called for them to be freed.
One of the activists said they were treated roughly by the special forces officers who escorted them back to jail after the sentencing. The women were transported in a bus full of burly officers, and two more buses carrying additional special forces troops drove along with them, Maria Alekhina wrote.
"To throw such resources at three women can mean only one thing: fear," Alekhina said in a handwritten note posted on the Internet by her lawyer. "And it's amazing to see the sweep of such fear."
The punishment of Pussy Riot has highlighted the crackdown on the opposition since Putin returned to the presidency in May.