Small protests are being reported in cities in the Russian Far East.
An Associated Press reporter saw about 50 protesters seized by police in the gathering at Mars Field.
Russian police detained opposition leader Alexei Navalny on Monday as he tried to leave his home ahead of a planned anti-Kremlin protest in Moscow, his wife said, but she called for the demonstration to go ahead all the same.
"Alexei was detained in the entrance hall of our building", his wife, Yulia, wrote on social media.
This was a reference to the main thoroughfare in central Moscow, near the Kremlin, where the protest was getting underway Monday afternoon.
Navalny was arrested outside his home en route to the rally. There was no immediate statement from police.
Electricity in Navalny's office was switched off, his spokeswoman said in a separate Twitter message.
But Navalny said late on Sunday that the authorities had pressured firms into refusing to supply him and his allies with sound and video equipment to make themselves heard and seen, a move he said was created to humiliate protesters.
Navalny's Fund for Fighting Corruption had been providing updates on protests throughout the country Monday.
On his website, Navalny urged his supporters to take to the streets and oppose Putin's government.
Mr Navalny got permission to hold the rally at another location but said he had moved it after authorities tried to "humiliate" protesters.
Navalny said contractors hired to build a stage at the agreed-upon venue couldn't do their work.
At the same time, police wouldn't interfere with participants marching down Tverskaya without placards and slogans, the Ekho Moskvy radio station cited a Moscow security official as saying.
Police have warned that they will take action if protesters break the law.
The protest was part of a day of demonstrations throughout Russian Federation spearheaded by Alexei Navalny, the anti-corruption campaigner who has emerged as Russia's most prominent opposition figure and who has announced he intends to run for president next year.
The Kremlin has long sought to cast the opposition as a phenomenon of a privileged, Westernized urban elite out of touch with people in Russia's far-flung regions.
The 41-year-old's anti-corruption videos have needled the country's most powerful and drawn to the streets crowds unseen since a wave of protests against President Vladimir Putin's reelection to a third term in 2012.