Ships in the region including Varna's anchorage and dock-side are reported to be unable to move safely as a result of unusually strong winds.
The Black Sea and Sea of Azov regions have been subjected to stormy weather with heavy snowfalls since the new year began.
Strong winds had forced the closure of five ports on Romania's Black Sea coast for more than a week while forecasters warned of heavier snowfalls and falling temperatures.
In the Kerch Strait, between the Black Sea and the Sea of Azov, at least four sailors died after their Bulgarian cargo ship, Vanessa, sank in a storm.