According to the independent legal organization OVD, the arrests must have taken place in almost 40 different cities.
Unsanctioned demonstrations are illegal under Russia's anti-protest laws.
In a televised speech on Wednesday morning, Putin announced that a decree on partial general mobilization had been signed and would come into effect today.
According to Russian Defense Minister Sergei Shoigu, the mobilization in the first stage means that 300,000 reservists will be called up.