Sixty survivors have been brought to a centre in Lampedusa, UNHCR spokesman Filippo Ungaro said.
According to survivor accounts, there were 92 to 97 migrants on board when the boat departed Libya.
Authorities were still searching for any remaining survivors.
The coast guard said in a statement that the death toll stood at 26, but was still "provisional and being updated".
Based on survivor accounts, about 95 migrants left Libya on two boats, International Organisation for Migration spokesperson Flavio Di Giacomo said.
When one of the two vessels started to take on water, all the passengers were transferred to the other boat - made of fibreglass - which then capsized because of overloading, he said.
It was not immediately known how long the migrants had been at sea.
Lampedusa mayor Filippo Mannino said that the shipwreck happened "presumably at dawn".
So far this year, 675 migrants have died making the perilous central Mediterranean crossing, not counting the latest sinking, according to the UN refugee agency.
"Deep anguish over yet another shipwreck off the coast of Lampedusa, where UNHCR is now assisting the survivors," Ungaro said on X.
In the first six months of 2025, 30,060 refugees and migrants arrived in Italy by sea, a 16 per cent increase compared to the same period last year, according to the UNHCR.
The migration route from northern Africa to southern Europe is considered one of the most dangerous in the world, with almost 24,500 people dying or disappearing on the Mediterranean crossing in the past decade, according to the IOM.
Most of the deaths have been attributed to small boats setting off from the coasts of Tunisia and Libya.
The deadliest shipwreck off the coast of Lampedusa occurred on October 3, 2013 when a boat carrying over 500 migrants from Eritrea, Somalia and Ghana caught fire and capsized, killing at least 368 people.
The tragedy prompted international calls for action to address the crisis.
