Safa Msehli, a spokesperson for the International Organization for Migration, said the vessel left the Libyan town of Khums on Sunday with about 75 men, women and children on board.
But on Monday the boat came to a standstill after it developed engine troubles, before capsizing in rough weather.
Only 18 people were plucked from the sea by fishermen and the Libyan coastguard and the others are presumed to have died.
Ms Msehli said survivors of the shipwreck who were successfully brought to shore reported there were at least 20 women and children among their fellow passengers who had not survived the sinking.
The tragedy is the latest in a series of disasters in the Mediterranean, as attempted crossings by refugees and migrants have soared in recent months.
The IOM’s Libya mission chief, Federico Soda, said on Twitter: “Horrified by yet another painful loss of life off the Libyan coast,”
“At least 57 people drowned today in the latest tragedy in the Central Mediterranean. Silence and inaction are inexcusable.”
According to the UN organisation, 891 people have died in the Mediterranean in the first six months of 2021, more than double the number in the same period last year.
Libya has for several years been the predominant launching pad for migrants hoping to escape poverty and conflict in Africa for a better life in Europe, by making the perilous sea crossing.
However, unscrupulous people smugglers often pack far too many migrants into decrepit boats, which are unable to cross the Mediterranean without sinking.
But life for those picked up from the shipwreck and returned to the Libyan coast may not be much better.
Amnesty International has said that in the first six months of this year, more than 7,000 people intercepted at sea were forcibly returned to detention camps in Libya.
Human rights groups and UN officials have long cited testimony from survivors who report systematic abuse - including rape, torture, forced labour and beatings - at these camps, as well as extortion by the traffickers who try to extract vast sums from desperate migrants before letting them attempt to cross the Mediterranean into Europe.