Eleven people survived the accident that occurred on Monday evening, said police spokesman Brenda Muntemba on Wednesday.
Police have so far retrieved 24 bodies from the lake, Muntemba told AFP.
She said the rescue team is now searching for 16 bodies, which are still missing. The boat was carrying about 51 people when the accident happened on Lake Mweru in Zambia's northern Luapula province near the border with the Democratic Republic of Congo.
The boat, which was carrying mostly fishermen was headed for the islands around the lake where people trade goods in exchange for fish, Muntemba said.
The Zambian government has dispatched a team of specialists to help manage the disaster.