A group of unidentified hooligans sprayed the monument at the Schwarzenbergplatz in the center of the Austrian capital with black paint late Wednesday.
The protest note demands that the incident be thoroughly investigated and the perpetrators be bought to justice. The document expresses the hope that Austrian authorities will do everything possible to prevent such incidents in the future.
Russia informed the Austrian Interior Ministry about the incident shortly after the crime was discovered early Thursday.
Austrian police responded immediately and had the monument cleaned within an hour and a half after being informed by Russia.
In line with an agreement signed on May 15, 1955 Austria is obliged to maintain all military cemeteries and monuments of allied nations on its territory.
Austria said last year it had been "dutifully fulfilling these obligations and continues to properly maintain the Red Army monument on Schwarzenbergplatz Square in Vienna and the burial places of fallen soldiers."