There were "more than a hundred passengers" on board the vessel when it sank on Thursday afternoon near Ukara Island in the southeast of the vast lake, which also extends into Uganda and Kenya, a local official said.
"It is feared that a significant number have lost their lives," said George Nyamaha, the head of Ukerewe district council of which the island is a part.
Regional governor John Mongella said late on Thursday the toll had reached 44 while 37 others had been rescued, though some of the survivors were in "a very bad condition".
He added that rescue operations had been suspended and would continue on Friday morning.
A statement from Tanzania’s Electrical, Mechanical and Services Agency said it was unknown how many passengers were aboard the MV Nyerere.
The ferry was also carrying cargo, including sacks of maize and cement, when it overturned close to the dock.
The cause of the accident was not immediately clear, but overloading is frequently to blame for such incidents.
President John Magufuli’s spokesman Gerson Msigwa also said on state television TBC 1 that the death toll stood at more than 40.
With a surface area of 70,000sq.km, oval-shaped Lake Victoria is roughly the size of Ireland.
Capsizes are not uncommon in the massive lake, and the number of fatalities is often high due to a shortage of life jackets and the fact that many people in the region cannot swim.
The deadliest such accident in recent decades was in May 1996, when around 800 people died after their ferry sank on its way to Mwanza in Tanzania.
Waters in the lake can be rough and boats are frequently poorly maintained, while ferry operators often fail to record the number of passengers on board.
Around 20 people were killed in December 2016 when their boat overturned in Lake Victoria as it was carrying passengers to Uganda’s mainland for Christmas holidays. — AFP/VNS.