The police moved in to disperse the rally, organized by Other Russia, when protesters tried to march to the Central Election Commission building.
Activists from the radical National Bolshevik Party were also arrested.
Moscow city authorities had allowed the rally but forbade demonstrators from marching to the commission building.
Police have broken up several so-called Dissenters' Marches in the past year, beating demonstrators with truncheons and detaining many.
A correspondent for RFE/RL's Russian Service reported that there around 1,000 opposition activists on the scene, while officials put the figure much lower.
Russia holds parliamentary elections on December 2, which the pro-Putin Unified Russia party is expected to win.
Other Russia is a broad coalition, united by its opposition to the Kremlin.
Speaking at the rally today, Kasparov said that if the current regime is preserved, "it will be a threat to Russia's existence."
"That is why our main purpose, from our point of view, is to dismantle the existing regime, the regime which is corrupt, criminal, and deceitful. The regime which cannot solve or raise the problems which should be discussed by the people of the country today," Kasparov said.
A number of other political groups held separate rallies in Moscow today, including the pro-Putin youth group Nashi and the Communist Party.