STORY: The independent OVD-Info protest monitoring group said it was aware of detentions in at least 36 different cities.
Unsanctioned rallies are illegal under Russia's anti-protest laws.
Putin made the announcement in a televised address in which he also announced moves to annex swaths of Ukrainian territory and threatened to use nuclear weapons to defend Russia, declaring: "It's not a bluff".
In a country that counts millions of former conscripts as reservists, Putin's "partial mobilization" decree gave no clue as to who would be called up. Defence Secretary Sergei Shoigu said 300,000 people would be mobilized from a pool of 25 million. Contracts of professional troops would be extended indefinitely.