Vladimir Kulishov, the first deputy head of Russia's Federal Security Service, said Russia had told the Royal Navy Type 45 Destroyer not to enter its waters, but that it had crossed what he said was the border on 13 October near southern Crimea.
The MOD said: "HMS Dragon was taking the most direct routebetween two port visits, navigating a recognised safe route for all international shipping within Ukrainian waters.
"The Russian Federation Navy did not impede HMS Dragon's passage.
"She navigated without incident, exercising our right of innocent passage under the UN Convention on the Law of the Sea."
Mr Kulishov told Russia's RIA news agency in an interview that Moscow had demanded the vessel immediately leave its waters, to which the warship's captain replied there was poor signal reception.
"The warship was driven out into neutral waters by the joint action of the Russian navy and air force," said Mr Kulishov.
Russia annexed the Black Sea peninsula of Crimea from Ukraine in 2014, drawing sanctions and condemnation from the West.