The court calls for his extradition to Russia and a two-month period of arrest.
Browder, once a major foreign investor in Russia, ran afoul of the government in the late 2000s while investigating an alleged large-scale tax fraud scheme with his lawyer Sergei Magnitsky.
Authorities seized Browder's company, Hermitage Capital, and denied him entry to Russia. Magnitsky was thrown in a Moscow prison, where he died in 2009.
Browder has since campaigned globally for sanctions against Russian human rights violators. Russia has placed him on the Interpol wanted list.