The dolphins' airways were clogged with oil, says Russian researcher Tatiana Belej according to state Russian media.
Russia has confirmed the oil spill but described it as partial and is still evaluating its scope.
Ukrainian authorities, on the other hand, have called the leak, which consisted of at least 3,700 tons of oil, extensive.
According to the organization Greenpeace, which is banned from operating in Russia, at least six miles of coastline are affected by the leak.
Russian media describe how thousands of people, many of them volunteers, are trying to clean up along the coast.
Media with a more critical stance towards the Kremlin have, however, quoted volunteers saying that state support is insufficient for the efforts required.
The Kerch Strait separates Russian-occupied Crimea from Russia and is an important global shipping route that has become central in Russia's war against Ukraine.
