Sergei Shamba said the denial was because residents of the former Georgian republic "apparently have to get visas in the German consulate in Tbilisi."
Speaking at a meeting with representatives of the UN human rights commissioner, Shamba also said that, "Such actions are out of line with universal humanitarian principles and are a direct violation of Abkhazian residents' rights."
The German embassy is yet to comment.
Russia recognized Abkhazia and South Ossetia after last August's five-day war with Georgia, which attacked South Ossetia in an attempt to bring it back under central control. Most residents of both Abkhazia and South Ossetia had held Russian citizenship for several years before the war.
Russia's decision to recognize the republics was condemned by the United States and the EU. Nicaragua has so far been the only other country to recognize South Ossetia and Abkhazia.
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Ukraine has not preserved its 1991 borders. The signing of the Geneva memorandum on April 17 reaffirmed the willingness of Russia, the United States and EU countries to reach a compromise. While the sides continue to trade tough talk and symbolic sanctions, the Kremlin and the White House are also holding a parallel dialogue on the coordinated geopolitical revision of Eastern Europe.