Local media reports said riot police scuffled with demonstrators as a few hundred people protested in Vladivostok, which is seven hours ahead of Moscow, and detained an unspecified number of people.
Navalny's anti-corruption videos have needled the country's ruling elite and drawn crowds to the streets not seen since the protests against President Vladimir Putin's reelection for a third term in 2012.
As police detained demonstrators, hundreds of others shouted slogans including "Putin is a thief" and "Shame!"
An actor, who takes part in the Russia Day festivities, walks past a police line in Moscow, Russia, Monday, June 12, 2017.
Police detained as many as 750 in Moscow and 900 in St. Petersburg, according to OVD-Info, an independent monitoring agency.
Police detain a protester in Moscow Monday.
Monday's protests could demonstrate that the opposition has significant support throughout the vast country.
The demonstrators appeared predominantly young - those who were born or grew up during Mr Putin's 17 years in power.
A photo of Navalny being bundled into a police vehicle was posted on Twitter by his wife Yulia, who said the protests were going ahead nonetheless.
The government had not approved the location of the protest and said it was unlawful.
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Russia's anti-corruption protests come in response to an investigation by Navalny's Anti-corruption Foundation into what was described as a corruption scheme in which Prime Minister Dmitry Medvedev was said to have amassed lavish mansions and taken luxury shopping trips.
"Since the 1990s, we have seen courageous women in Russia's civil groups and journalism, who choose to [take a] risk and make a difference because they are free people and want to live in a free Russian Federation", said Tatiana Lokshina, program director of Human Rights Watch in Moscow. Other protesters scaled a scaffold and hung a sign saying, "Only revolution will defeat corruption". About 150 protesters gathered in Cheboksary, Magnitogorsk and Ulan-Ude, about 200 met in Bryansk and Rostov-on-Don, and 300 people gathered in Tyumen.
More than 1,000 protesters were arrested at a similar rally on March 26. Authorities said 500 had been arrested during the demonstrations in St. Petersburg. Navalny, who is mounting a long-shot bid to replace President Putin in next year's election, has suffered a series of arrests for his protests against the state.
Navalny had called on supporters to gather starting at 2 p.m.in Tverskaya Street, a central thoroughfare, after complaining that the government prevented him from hiring a stage and sound equipment to hold his demonstration in an agreed location elsewhere in the city. But before he could even attend, Navalny was detained outside his home, accused of organizing a public rally without permission, sent to court and now faces a hefty fine. Moscow authorities reported that 300 had been detained. Many graduates of its prestigious university have left Russian Federation to work in the West.
Witnesses saw a police vehicle leaving Mr Navalny's apartment compound at high speed, followed a few minutes later by a minibus carrying around 10 police officers.
Monday is Russia Day, a public holiday, a factor that may boost turnout. We saw dozens of people plucked from the crowd - many of them young - and dragged roughly towards police buses.
Navalny was jailed for 15 days after the March protests.
Monday's protests were widely anticipated.
Moscow authorities had initially authorized a venue for the protest away from the city center.
The Moscow Prosecutor's Office warned Navalny that holding a demonstration on Tverskaya Street would violate the law and law enforcement would be compelled to take necessary measures.
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