To reach next summer's finals in Sweden the Russian team now has to defeat Spain on Tuesday.
The decision to ask the Russian soccer authorities to choose a neutral venue for the match, a qualifier for the Under-21 Euro 2009 tournament, was taken by an emergency UEFA commission in Monaco on Thursday.
Russia, the tie's nominal hosts, chose the Trud stadium in Minsk.
UEFA cited "the political situation between Russia and Georgia" as the reason for its decision.
Russia and Georgia fought a brief war after Tbilisi's invasion of South Ossetia in August and tensions between the two former Soviet republics remain high.
UEFA earlier ordered the Georgian national team to choose an alternative venue for Saturday's World Cup 2010 qualifier against the Republic of Ireland. The match will take place in the German city of Mainz.