Russia accused Ukrainian police of doing nothing to stop the attack, and called it a “grave violation of Ukraine’s international obligations”.
Meanwhile NATO released images which it says back up Ukrainian claims that Russian tanks crossed into Ukraine.
Moscow has denied sending the tanks to help pro-Russian rebels in the east.
A range of images show the T-64 tanks first at a Russian military staging area near Rostov-on-Don, and then apparently inside Ukraine earlier this week.
Unlike Ukrainian armored vehicles, the tanks have no markings or camouflage.
NATO says the pictures “raise significant questions” about Russia’s role in eastern Ukraine.
Saturday’s disturbance in Kiev occurred when several hundred protesters hurled eggs and paint at the Russian embassy.
One petrol bomb was also hurled, windows smashed and flags torn down.
The protesters – some wearing balaclavas – overthrew cars with diplomatic plates. One protester held a sign saying: “Russia is a killer.”
Russia’s protest against the incident was echoed by the US state department: “The United States condemns the attack on the Russian embassy in Kiev, and calls on Ukrainian authorities to meet their Vienna convention obligations to provide adequate security.”
Earlier on Saturday, Ukrainian President Petro Poroshenko vowed to retaliate against pro-Russia separatists in the east after a military plane was shot down by anti-aircraft fire, killing all 49 people on board.
The Ilyushin-76 transport was attacked by separatist forces as it was about to land in the city of Luhansk.
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