Protesters in Moscow had camped at the front and rear of the Estonian embassy building, ignoring EU appeals to respect an international treaty guaranteeing the protection of diplomats and embassies.
'Fascism won't pass'
On Wednesday, protesters chanting "Fascism won't pass" stormed a news conference by the Estonian ambassador, before bodyguards used gas to disperse them.
Marina Kaljurand, the Estonian ambassador, said that during the night, stones had been thrown at the embassy compound, breaking four windows.
Russia has grown increasingly sensitive to what it sees as Nato's encroachment on it's traditional turf and expansion into its former territories.
Estonia joined Nato and the EU in 2004.
Earlier on Wednesday, the Russian Foreign Ministry summoned the ambassadors of Germany, the EU and Portugal to express "deep bewilderment" about what it termed the "lack of a principled assessment by the European Union of the actions of the Tallinn government".
Also, Sergei Lavrov, Russia's foreign minister, called Urmas Paet, his Estonian counterpart, to "warn the Estonian leadership to refrain from provocative actions that may further exacerbate the situation".
The crisis began last week when Estonia moved a bronze statue of a Red Army soldier, a symbol of the huge number of Russian deaths in World War Two, to a military cemetery.
Estonia, which was annexed by Moscow in 1940 and achieved independence in 1991, also began uncovering the remains of 12 Soviet soldiers buried underneath the statue.
Many Estonians view the monument as an unwelcome reminder of almost 50 years of Soviet rule and want it removed from its prominent location in their capital city.
However, many ethnic Russians, who make up about a third of Estonia's population, have protested against the memorial's removal to a military cemetery.
Traders said on Wednesday that Russia had halted rail deliveries of oil products and coal to Estonia.
Russia's record of using energy resources for political ends prompted speculation that the move was retaliation for the monument's removal.
But railway officials cited planned annual maintenance as the reason and denied any political motive.