Kasparov and other critics of Russia's current leadership were arrested for "attempts of hooligan and illegal actions, said Viktor Biryukov, a spokesman for the Moscow police.
The protesters were arrested as they approached Trifainaya Square in Central Moscow, CNN reported. In addition to Kasparov, Eduard Limonov, founder of the opposition coalition called The Other Russia, was also arrested.
Kasparov, who leads the United Civil Front Party, and Limonov want to "peacefully dismantle" what they say is the illegitimate rule of Russian President Dmitry Medvedev and Prime Minister Vladimir Putin, Interfax said.
Russia has been put on the "edge of catastrophe" by the failing economy and Medvedev and Putin's leadership, Kasparov said.
Celebrity Breakups and divorces of 2014 [PHOTOS]