In a push to galvanise support, Navalny's team released a video about an opulent palace on the Black Sea they alleged belonged to Putin, something the Kremlin denied.
Navalny is believed to have been poisoned last August with a toxic nerve agent used in chemical weapons.
His arrest drew widespread Western condemnation, with the United States, the European Union, France and Canada all calling for his release.
Navalny's associates urged Russians to take to the streets despite official pressure and promised financial help to protesters given fines on Saturday. Previous large-scale opposition demonstrations in 2012 and 2019 were largely centralised in Moscow.
The gamble puts the Kremlin in a quandary as to how it responds, nine months before parliamentary elections.
Some were beaten with batons. "The light in the police van is very poor", she wrote in the caption.
"Criminals dressed in uniforms are protecting criminals at the helm", Vera Spivakova, a 71-year-old pensioner, told AFP in Moscow.
The 44-year-old says the charges are politically motivated.
The first protests took place in the Far East and Siberia including Vladivostok, Khabarovsk and Chita where several thousand took to the streets, Navalny supporters said.
The US embassy in Moscow, however, said Saturday it was following the rallies, adding that Washington supported "the right of all people to peaceful protest, freedom of expression".
In a video message on the sports.ru website, Denisov said he had "great respect" for Navaly - an unusual step for Russian athletes who usually toe the Kremlin line.
A Radio Free Europe (RFE) journalist tweeted a video showing Moscow police kneeling on the neck of a protester.
The West has told Moscow to let Navalny go, sparking new tensions amid already strained Russian ties as US President Joe Biden launches his administration.
Navalny made his allegations in a video his team released online, which has been viewed more than 35 million times.
The OVD-Info protest monitor group said that at least 1,090 people, including 300 in Moscow and 162 in St. Petersburg, had been detained across Russian Federation, a number likely to rise. He says it is a trumped-up case created to silence him, and has called on his supporters to protest.
One driver had hung a pair of underpants out of his vehicle window, a reference to Mr Navalny's poisoning.
"Senior officials in the USA embassy will have to have a serious conversation with the Russian foreign ministry", it said in a statement. Prosecutors and police called the planned rallies illegal, and colleges threatened to expel students who attended them. Media estimates ranged from 15,000 to 40,000, and the Proekt investigative website said Moscow and St. Petersburg saw their biggest unauthorized protests in nearly a decade.
Russia's interior ministry said 4,000 had turned up in Moscow, but opposition sources say it may be as high as 15,000.
Attendees at a small protest in the Siberian city of Yakutsk saw temperatures dip as low as -50C (-58F).
The Russian media regulator Roskomnadzor - which has threatened to fine social media companies over protest-related content - said on Friday that TikTok had taken down 38% of posts calling on minors to participate in the demonstrations.