Russia registered Carnivac-Cov in March after tests showed it generated antibodies against Covid-19 in dogs, cats, foxes and mink.
The first batch will be supplied to several regions of Russia, the regulator Rosselkhoznadzor said in a statement.
It said companies from Germany, Greece, Poland, Austria, Kazakhstan, Tajikistan, Malaysia, Thailand, South Korea, Lebanon, Iran and Argentina had expressed interest in purchasing the vaccine.
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The World Health Organisation has voiced concern over the risk of transmission of the virus between humans and animals. The Russian regulator has said the vaccine would be able to protect vulnerable species and thwart viral mutations.
"About 20 organisations are ready to negotiate registration and supply of the vaccine to their countries. The file for registration abroad, in particular in the European Union, is under preparation and will be promptly used for the registration process," the Russian watchdog said.
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