Their metal boat overturned during bad weather during the night of Thursday to Friday after setting off from the Tunisian port of Sfax, said a joint statement from the UN agencies for refugees, children and migration.
The survivors — a 13-year-old boy on his own, a woman and two men — were rescued by a merchant ship and brought to Lampedusa by the Italian coastguard, they said.
In a separate statement, the Italian Red Cross, which manages the migrant reception centre on the island, said the four were generally in good health.
It confirmed the testimony that there had been 45 people on the boat when it went down, adding that none of those missing were related to the survivors.
The four managed to survive the shipwreck by floating on inner tubes, it said.
The shipwreck is one of several deadly incidents reported in recent days after a period of bad weather.
Officials on Monday had reported that 16 migrants died in shipwrecks off the coasts of Tunisia and Western Sahara.
And on Sunday, the UN’s migration agency, the International Organization for Migration (IOM), said at least 30 people were missing after two shipwrecks off Lampedusa.
The tiny island, located just 90 miles (around 145 kilometres) from Tunisia, is the first port of call for many migrants heading from North Africa to Europe.
But many of them do not survive, making the Central Mediterranean migrant crossing the world’s deadliest.
More than 1,800 people died attempting the route so far this year, according to IOM figures from Friday — the toll from the latest shipwrecks brings that to almost 1,900.
This is more than double the same period last year, IOM spokesman Flavio di Giacomo said, adding that this was likely to be an underestimate.
