Italian officials said at least a dozen other people are still missing.
The boat tipped over in bad weather near the Italian island of Lampedusa.
The UN says more than 1,000 people have died in the Mediterranean so far this year trying to make the perilous journey to Europe.
Italy's coastguard said it had launched a rescue mission late on Sunday after being alerted to an overloaded and badly listing boat about six nautical miles (11km) from Lampedusa.
But as the rescue ships approached shortly after midnight on Monday, "adverse weather conditions and the sudden displacement of the migrants" caused the boat to capsize, it said.
The boat had earlier left the Tunisian coast with about 50 people on board, Italian media reported.
Rescuers pulled 22 people alive from the water and recovered the bodies of the 13 women. Those still missing include at least eight children, survivors said.
An Italian prosecutor has arrived on Lampedusa to open an investigation, the Ansa news agency reported.
Thousands of migrants attempt to cross the Mediterranean to Europe every year. Those who make the journey often travel in poorly maintained and overcrowded vessels, and many have died en route.
Last month, France and Italy called for a new system to automatically redistribute migrants across the EU as the number of people entering Europe via Italy and Greece surged.