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.
"It shows that there may very well be shipwrecks we don't know about, because the boats sink without a trace," Flavio de Giacomo, an IOM spokesman, told AFP.
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.
Migrants keep coming
Last week, the Spanish group Pro-Activa Open Arms discovered two empty and partially capsized dinghies, raising fears that hundreds of migrants could be missing, since smugglers often pack 120 to 140 people on such vessels, and often many more.
But these incidents are not included in the IOM's estimates, in particular as one of the vessels may have been one that capsized in Libyan waters shortly before then, in which 54 people were rescued but 66 were missing.
The dangers have not slowed the surge in arrivals this year, however: The Italian coastguard says it orchestrated the rescue of more than 1,100 migrants off Libya between Tuesday and Wednesday morning.
The coastguard is taking them to Sicily, which will bring the total number of arrivals to Italy this year to more than 24,000, a sharp increase from the same period last year.
Nongovernmental organisations say the increase reflects worsening living conditions in Libya as well as fears, whipped up by smugglers, that Europe will soon block off the Mediterranean passage for good.
Italy has been trying to bolster its cooperation with Libya to halt the people-smuggling operations by building camps to house migrants who are intercepted trying to reach Europe, and send them back to their countries.
The plan has riled rights groups, who see the potential for abuse in Libya and note that 40 percent of sub-Saharan migrants who apply for asylum in Italy are currently being accepted.