A food delivery man leaves an exchange office with screen showing the currency exchange rates of U.S. Dollar and Euro to Russian Rubles in Moscow, Russia, Thursday, Feb. 24, 2022. AP
The Investigative Committee, a government body that investigates major crimes, warned Russians of legal repercussions for joining unsanctioned protests related to "the tense foreign political situation".
It said it was responding to social media calls to protest against Putin's decision to attack Ukraine.
"One should be aware of the negative legal consequences of these actions in the form of prosecution up to criminal liability," it said.
The Russian interior ministry said it will take "all necessary measures to ensure public order."
Russia has strict protest laws and demonstrations often end in mass arrests.
Some Russians called on social media for people to take to the streets to protest against the Ukraine attack.
Independent rights monitor, OVD-info, said at least 27 people had been arrested throughout Russia for holding anti-war protests.
Jailed Russian opposition leader Alexei Navalny said earlier on Thursday that he was against the invasion in a speech during his trial, held behind bars.
"I am against this war," Navalny was heard saying in a video published by independent news outlet Dozhd.
"This war between Russia and Ukraine was unleashed to cover up the theft from Russian citizens and divert their attention from problems that exist inside the country," Navalny said.
Putin launched an offensive on Ukraine in the early hours of Thursday after a national address aired at around 5:40 am local time (0240 GMT).