Some 1,700 people were detained in Moscow alone, Ria news agency reports, citing the interior ministry.
The OVD-Info rights group says detentions took place in 53 cities.
Although protests have become increasingly restricted in recent years, numerous rallies have taken place across Russia since the invasion.
In the last 11 days, more than 10,000 people have been detained at protests, OVD-Info says.