Mainly Russian-speakers, about 300,000 in a country of 1.3 million, rioted on Thursday and Friday over the monument being removed from the city centre.
Estonia's prime minister called the demonstrators "drunken hooligans", and the dispute has shown the depth of feeling among Russians, who wanted the statue to stay, and Estonians, who generally backed its removal.
Estonia's foreign ministry said it had sent a note to Russia "which voiced the utmost indignation and protest in relation to the ever-increasing attacks" against its embassy.
The crowd outside the embassy was about 200-strong on Monday afternoon, mainly young activists.
Franek Persidski, the embassy spokesman, said the youths, now in a fourth day of protest, played loud music around the clock and had hurled stones, paint and eggs at the building.
In the Ukrainian city of Kiev, news agency Interfax said police used tear gas on demonstrators throwing objects at the Estonian embassy.
Russia has protested against removing the monument as an insult to the memory of soldiers who fought against fascism.