Local media report that the boat capsized in rough waves on the stretch between the town of Kariba in northern Zimbabwe and a fishing camp.
The boat has a capacity for 90 people, but the country's rescue service says ticket sales show that 119 adults, including five crew members, were on board. There may also have been an unknown number of children under the age required to have a ticket on board.
77 people have been rescued.
Lake Kariba is the world's largest artificial lake by volume.
