"We are expressing condolences to the family and friends of the killed citizen and demanding Estonian authorities provide full information on what happened, promptly conduct an investigation and bring those guilty to justice," the ministry said.
The ministry said Tallinn has not named the Russian, who had permanent residency in Estonia and was killed in the early hours of Friday, or provided the circumstances of his death so far, while also condemning the excessive use of force against people who defended the monument to fighters against Nazism.
Latest police reports said about 800 people had been arrested between Thursday night and Saturday morning in Tallinn, where police used tear gas and water cannons to disperse protestors, who shattered windows in buildings near the Soviet Bronze Soldier statue in the city center, damaged bus stops and parked cars and set billboards on fire. Sixty people, including police officers, have been injured.
Estonian police have not disclosed the whereabouts of those arrested.
"After consultations with the prosecutor's office, we made a decision that police should not disclose where people detained during mass riots on Thursday and Friday are being held," Taavi Kullerkupp from the press service of a police precinct in Tallinn said Saturday.
The protests erupted after Estonian authorities cordoned off the area around the Soviet World War II memorial Thursday in the run-up to Victory Day May 9. They moved to dismantle and relocate the Bronze Soldier late Thursday, when protests turned into violent riots.
Estonia has said the Bronze Statue and other Soviet monuments - rallying points for ethnic Russians and places of their clashes with Estonian nationalists - "divide society," and the central square is not a proper burial place.
The Foreign Ministry said Russia, which has repeatedly voiced concerns over discrimination against ethnic Russians in Estonia and the other ex-Soviet states in the Baltics, hoped "international, above all European, organizations and European officialdom will take a sharply critical position [on the events in Tallinn] without double standards."
European bodies have made no comment on the dismantling of the monument in EU member Estonia so far.