Rescue operations are underway, but those who have disappeared are "probably dead," a coastguard spokesman said.
A coast guard official on Thursday said close to 100 migrants were feared missing after their boat sank off the Libyan coast near Tripoli.
Coast guard spokesman Ayoub Qassem said 23 migrants were rescued from the craft off Gargaresh, a western suburb of Tripoli.
The boat's hull was completely destroyed and the survivors, all men, were found clinging to a flotation device, Qassem said.
The missing include 15 women and five children, he said.
Those who had disappeared are "probably dead," but bad weather had so far prevented the recovery of their bodies, he added.
More than 24,000 migrants arrived in Italy from Libya during the first three months of the year, up from 18,000 during the same period last year, according to the UN High Commissioner for Refugees.
Libya has become a key departure point for refugees as more than 150,000 have made the crossing from Libya to Italy in each of the past three years.