According to Denmark's body overseeing sea navigation, the sub (NATO codename Whiskey) was being tugged from a Polish shipyard.
Some 55 kilometers (34 miles) from the Danish coast, the submarine began taking on water and the tugboat crew had to disconnect the towing cable as the ship sank.
There were no people, arms or fuel onboard the submarine, and the vessel does not pose an environmental hazard, Danish authorities said.
However, because the submarine sank to a depth of about 25 meters (75 feet), it represents a potential obstacle to navigation, and authorities have promised to salvage it.
A total of 236 diesel electric submarines of Project 613 (Whiskey class) were built in the Soviet Union between 1949 and 1957, based on German Type XXI submarines.
The U.S.S.R. gave 45 such subs to allied and friendly nations.
