Critics say the planned constitutional change to extend the presidential term is part of a concerted effort to retreat from democratic ideals, and is aimed at strengthening the powers Vladimir Putin, the former president who is now prime minister.
Before the scheduled start of the protest, hundreds of officers guarded Triumph Square, which was ringed by police trucks and metal barriers.
Police grabbed protesters who tried to enter the square, dragging them into waiting trucks.
According to Marina Litvinovich, an Other Russia spokeswoman, said "today we saw a police state and its methods".
Popular support for Other Russia and various opposition groups is minimal, but the Kremlin is wary of public anger as its struggles with a potentially politically damaging economic downturn.
Kasparov and other prominent activists have just launched a new anti-Kremlin movement called "Solidarity" in a bid to unite Russia's opposition forces and encourage a so-called "popular revolution" similar to those in Ukraine and Georgia.