The RCFS monitors human rights in Chechnya.
An Amnesty International spokesperson said the decision appears to be "the latest move in a carefully calculated strategy to get rid of an organization that has been outspoken on behalf of victims of human rights violations in Chechnya."
The court based its decision on a law that makes it illegal for a nongovernmental organization to be headed by a person convicted of "extremist" activities.
The executive director of the RCFS, Stanislav Dmitrievsky, was convicted in February for publishing articles by Chechen separatist leaders.
Amnesty International said the conviction violated Dmitrievsky's peaceful exercise of his right to freedom of expression.
The aftermath of a December 2002 Chechen resistance attack on the main government building in Grozny (epa)