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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The clash of Russian and Western interests has given rise to a geopolitical battle. German politicians are trying to leave all doors and windows open for dialogue with Russia. Moscow does acknowledge this, and Germany is probably the only country with which it is ready to discuss European security.