The border guards have said that Russian servicemen are in control of the Crimean side of the narrow channel and that Russian armoured vehicles have been sighted on the Russian side.
"The Kerch Strait is blocked by two Russian ships - from the north and from the south," Pavel Shishurin, the deputy head of the border guards, told reporters.
The Russian military has not confirmed his comments.
The Kerch Strait provides access to the Black Sea for ships carrying grain and other commodities from southern Russian regions.
But a Ukrainian border guard spokesman said: "The action (blockade) does not affect civilian shipping."
The Ukrainian infrastructure ministry also said that non-military vessels could use the strait as usual.