The ship was on its way to Europe from the port in the city of al-Khums in Libya when the accident occurred.
There must have been about 120 people on board, several of them women and children.
At least 74 people have drowned and 47 have been rescued by Libyan coastguards and fishermen, according to the UN migration agency IOM, according to the news agency Reuters.
"Vulnerable people have to pay the price"
Since the beginning of October, at least eight ships carrying migrants have capsized in the central Mediterranean, according to the IOM.
In the last two days alone, two other similar accidents have claimed at least 19 lives.
At least 900 lives have thus been claimed during attempts to reach the shores of Europe so far this year.
"Thousands of vulnerable people continue to pay the price for passivity both at sea and on land," Federico Soda, IOM's Libyan chief, said in a statement.