The ferry MV Nyerere capsized just a few metres from the dock on Ukerewe, the lake's biggest island, which is part of Tanzania. Initial estimates suggested there were more than 300 people on board.
In an address to the nation on state-owned broadcaster TBC in which he declared four days of mourning, Magufuli said: "We have directed that all individuals who were involved in causing this accident to be arrested."
"I have information that some have been arrested including the captain who, I am told, was not on board."
With some opposition politicians saying the government responded late to the sinking, Magufuli warned against politicizing the disaster.
"Let's leave designated authorities to investigate," he said.
Lake Victoria, Africa's largest, has a length of more than 200 miles (33k kms) and is 160 miles (250 km) across at its widest point.
Tanzania has been hit by several major ferry disasters over the years. At least 500 people were killed when a ferry capsized on the lake in 1996. In 2012, 145 people died when a ferry sank off the shore of the archipelago of Zanzibar.
State-owned Habari Leo reported on its website on Friday that top officials of the Surface and Marine Transport Regulatory Authority (Sumatra) would be questioned in regard to the accident.
Preliminary investigations, the paper said, showed the ferry had carried more passengers than its capacity permitted.
Thirty-seven people had been rescued from the lake, Jonathan Shana, the regional police commander for the port of Mwanza on the south coast of the lake told Reuters.
Shana said more rescuers had joined the operation when it resumed at daylight on Friday. He did not give exact numbers.
The precise number of those aboard the ferry when it capsized was hard to establish since crew and equipment had been lost, officials said on Thursday.