Emergency services say the accident was caused by the vessel being overloaded. The boat carried 37 people when it capsized, more than twice the maximum number of 15 people allowed.
The boat's captain has been detained.
The Ivolga capsized last evening in a storm near the major port city of Odessa.
Olga Shevchuk of the state emergency services said Sunday that the death toll rose overnight to 14, while 19 of the 23 people who were saved remained hospitalised.
A photo of the boat published by the Ukrainian news agency Unian showed it as a small motor vessel with awning-shaded viewing areas both fore and aft.