Under the document, valid until December 1, 2011, the government is to develop ways to restrict military cooperation with countries supplying Russian or Soviet-made arms to Georgia.
Countries or individuals found to be in breach of these regulations will face economic and financial sanctions.
The Kremlin said the decree had been signed to protect Russia's national interests.
Relations between Moscow and Tbilisi have been strained since Georgia attacked South Ossetia on August 8 in an attempt to regain control over the breakaway republic, which split from Georgia in the early 1990s. In response, Russia launched a military operation to eject Georgian troops from the region.
Russia recognized the independence of South Ossetia and Abkhazia, another separatist republic, on August 26.
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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.