The court identified the six men as Mikhail Golovachuk, Ruslan Khansvyarov, Dmitry Korotayev, Alexei Malozemov, Artyom Zayets and Daniil Puzyrevsky.
In a rare apparent demonstration of U.S.-Russian collaboration at a time of high tensions between the two over Ukraine, Russian authorities detained and charged the REVil group's members this week.
A police and FSB domestic intelligence operation searched 25 addresses, detaining 14 people, the FSB said on Friday, listing assets it had seized including $600,000 of computer equipment and 20 luxury cars.
The United States welcomed the arrests.
The United States said in November it was offering a reward of up to $10 million for information leading to the identification or location of anyone holding a key position in the REvil group.
A source familiar with the case told Interfax the group's members with Russian citizenship would not be handed over to the United States.
(Reporting by Andrey Ostroukh and Polina Nikolskaya, editing by Ros Russell)