Seventy-seven people were rescued and were taken to an island on the lake, the national disaster management agency said.
But the statement by Zimbabwe's Civil Protection Unit added it could only confirm there were 114 adult passengers onboard, along with five crew members through confirmed ticket sales.
There could have been an unknown number of children below ticketing age who were onboard and not accounted for, it said.
The boat has a carrying capacity of 90 people, the agency said.
Mutsa Murombedzi, a local member of parliament, posted a video of what she said were people on shore waving off what appeared to be the ageing ferry at the start of its journey.
She said rural communities use the boat to travel along the lake to the town of Kariba.
Some people standing on the shore were also concerned if the ferry would survive strong waves on the lake, according to the video.
Earlier, Zimbabwe police said a rescue operation was underway but did not give any other details.
Zimbabwean state broadcaster ZBC published video of speedboats making their way to what appeared to be an overturned boat on the lake as a helicopter hovered overhead.
Lake Kariba in southern Africa forms part of the border between Zimbabwe and neighbour Zambia.
It is the largest man-made lake in the world by volume and was created in the late 1950s and early 1960s by building a dam wall to block the Zambezi River, resulting in a valley slowly filling with water to form a huge lake that's now more than 200km long and up to 40km wide in places.
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