About 150 people rallied outside the Russian embassy in Kiev on Sunday night and an embassy car was set alight.
Anger erupted after Russia used weapons on two Ukrainian small warships and a tugboat as they were heading through the Kerch Strait, a narrow waterway that gives access to the Sea of Azov, used by Ukraine and Russia.
Russia claims the ships entered its waters illegally.
Ukraine said six of its soldiers were injured, two seriously, but Russia's FSB reported only three had suffered non-life threatening injuries and were given medical treatment.
The confrontation in waters off the Crimean peninsula marks a major escalation in tension in the long-running conflict pitting Ukraine against Moscow and Russian-backed rebels in the east of the country.
The seizure has sparked alarm among Kiev’s Western allies.
“We expect Russia to restore freedom of passage at the Kerch strait and urge all to act with utmost restraint to de-escalate the situation immediately,” the European Union said in a statement.
The UN Security Council is to hold an emergency meeting on Monday, on the request of both countries, to look into what happened.
During a meeting of Ukraine's National Security and Defence Council, President Petro Poroshenko described the Russian actions as "unprovoked and crazy".
He vowed to ask parliament to introduce martial law but underlined that this did not mean a "declaration of war". "Ukraine does not plan to fight anyone," he said.