Since the beginning of this year, at least 590 migrants have died or gone missing along the Libyan coast.
The man was rescued by a Spanish military ship participating in the EU's "Operation Sophia" to crack down on smugglers, and then brought to the Italian island of Lampedusa.
The vessel left on Sunday or Monday from Sabratha, western Libya, with five children and several pregnant women among those on board, the Gambian told a member of the UN High Commissioner for Refugees who met him at a hospital in Lampedusa.
Most of the passengers were from Nigeria, Mali and The Gambia, he said.
He said that the boat began taking on water a few hours after setting off, and that he survived by holding on to a fuel can.
According to information gathered by the International Organization for Migration (IOM), the man was spotted almost by accident by the Spanish ship, which then transferred him to the Italian coastguard.
Since the beginning of this year, at least 590 migrants have died or gone missing along the Libyan coast, excluding this latest capsizing, the IOM estimates.
The Italian authorities say more than 23,000 migrant arrivals have been registered on their coasts this year.