"Alexei has been detained in the stairwell", she wrote about 40 minutes before an anti-corruption rally called by the Kremlin critic was set to start in the city centre. "He asked me to tell you that the plans (for the protest) are unchanged".
There was no immediate comment from police on why Navalny had been arrested or where he was taken.
Tverskaya, known in Soviet times as Gorky Street, was closed off to traffic on Monday for an extensive commemoration of the national holiday Russia Day, including people dressed in historical Russian costumes.
Navalny said protesters had a constitutional right to gather to express their political opinions and that Tverskaya Street would be an ideal location because it will be turned into a pedestrian zone for the Russia Day celebrations.
Meanwhile Navalny's YouTube channel, which had been broadcasting live to more than 50,000 people as protests across Russian Federation got underway, lost light and sound in the studio.
A live internet feed run from the opposition leader's office went offline and his spokeswoman said electricity to the office was cut.
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Several people were arrested earlier today at protests in the east of the country, with at least eleven being detained at a rally in the city of Vladivostok.
Authorities in Moscow had authorized a venue for the protest away from the city center.
After the change, Moscow police warned that "any provocative actions from the protesters' side will be considered a threat to public order and will be immediately suppressed". Authorities had given permission for the rally, but Navalny late Sunday called for the location to change to one of Moscow's main avenues. Two large men stood nearby as Navalny spoke, insisting he will "say obvious banal things, but not be afraid and say them out loud". It remains unclear too whether the Kremlin will let Navalny run for the presidency.
Demonstrations were being held or planned in more than 200 cities and towns to protest what Navalny says is a system of corruption and cronyism that President Vladimir Putin presides over.
For now, polls suggest Navalny has scant chance of unseating Putin, who enjoys high ratings.
Medvedev dismissed Navalny's allegations as politically motivated "nonsense" and called the opposition politician a muck-raking charlatan.