Speaking on the first day of hearings, Tina Burjaliani, the Georgian first deputy of justice, said: "At the present time there are approximately 450,000 Georgians who have been expelled from their homes and villages and forced to seek refuge elsewhere in Georgia."
She said that due to a "real and imminent threat", Georgia was seeking the urgent assistance of the court.
The court will hold three days of emergency hearings after Georgia demanded that Russia ensure that no ethnic Georgians are "subject to violent or coercive acts of racial discrimination, including... death or bodily harm, hostage-taking and unlawful detention".
Russia will present its defence later on Monday, with further hearings to follow on Tuesday and Wednesday.
Moscow is expected to question the jurisdiction of the ICJ during the hearings, and may also dispute Georgia's claims that ethnic discrimination is occurring, or argue the situation is beyond its control.
Speaking on the sidelines of the hearing, Russia's ambassador to the Netherlands, where the case is being held, denied the charges and said Russia was not in breach of the discrimination convention.
Kirill Gevorgian said: "That is not true and we will produce facts and evidence that it is not true."
Georgia filed its lawsuit last month shortly after Russia invaded Georgia after Tbilisi tried to recapture South Ossetia by force.
Georgia alleges that Russia violated an anti-discrimination convention during three interventions in South Ossetia and Abkhazia from 1990 to August 2008.
Moscow drew condemnation from the West last month after it sent its forces beyond the disputed areas.
Russia later recognised the breakaway regions as independent states.
The court hearings began as Nicolas Sarkozy, the French president, travelled to Moscow for talks with Dmitry Medvedev, the Russian president, to assess Russian compliance with a French-brokered peace plan that helped end the conflict.