The German volunteer group ResQship told the AFP news agency that it managed to rescue 22 people on board the Nadir and then took these survivors to the town of Lampedusa in Italy.
The survivors were men, women and children from Cameroon, Côte d'Ivoire and Mali, says the captain of the Nadir, Ingo Werth.
The remains of two men were recovered by Nadir's crew.
The migrant boat sank on the night between Saturday and Sunday and the victims had been in the water for two hours before Nadir arrived.
In total, about 40 migrants had been on board the boat when it left the port city of Sfax in Tunisia. It is believed to have cost them just over SEK 10,000 each to get a seat on board for the trip.
In recent days, thousands of migrants have crossed the Mediterranean from Tunisia to Lampedusa. Sunday's incident is one in a series of tragedies in which dozens of people drowned or frozen to death trying to reach Europe.