The overcrowded boat was carrying 130 people and many of those who drowned on Sunday were children, local online outlet TV Diario Nampula reported.
The boat was operating between Lunga and the Island of Mozambique in Nampula province in the north of the country when it capsized, the report said.
Rescue efforts continued on Monday, with people still feared missing.
Some people had been travelling to attend a fair while others were trying to "flee from Lunga to the Island of Mozambique for fear of being contaminated by cholera, which has affected that region in recent days", media reported.
Other news reports quoted Jaime Neto, the secretary of state in Nampula province, as saying that misinformation about an alleged cholera outbreak caused people to panic and board the boat, which ordinarily serves as a fishing vessel, in an attempt to flee.
Mozambique and neighbouring southern African countries Zimbabwe and Malawi have in recent months been affected by a deadly cholera outbreak that authorities are battling to contain.
Many areas of Mozambique are only accessible by boats, which are often overcrowded.
The country has a poor road network and some areas are unreachable by land or air.
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