The court's action rejected the NGO's appeal against the inspection, which was conducted in March by the Moscow Prosecutor's Office and the Justice Ministry.
Evidence of the organization receiving foreign funding was found during the inspection, Memorial's press office told RIA Novosti.
Under a controversial law that went into effect in 2012, a politically active NGO with sources of foreign funding must register as a "foreign agent" and face increased scrutiny once registered. Many NGOs have refused to register, saying the title "foreign agent" discredits them, and that complying with increased monitoring is expensive.
Prosecutors said inspectors found the Memorial organization received about $3.2 million in foreign funding in 2010-2011 for a project to shape public opinion in Russia. That was before the NGO law took effect.
The prosecution said the center, apart from its educational and historical-awareness goals, was politically active because it tried to influence public opinion and policymaking.
The Memorial Human Rights Center, established in 1991, "appeals to society to not forget the cruel and massive human rights violations in our country's past, but also not to ignore that human rights violations continue to occur," its website says.