Those rescued from the fishing vessel off the coast of southern Sfax province included "Tunisians and foreigners", it said citing an initial toll.
The Tunisian national guard and navy units found the ship about 30 kilometres off shore after receiving a distress call at around midnight on Saturday.
The ministry said search operations, with the help of military aircraft and divers, were ongoing.
Tunisians and migrants regularly try to cross the Mediterranean to seek a better future in Europe, but departures peaked last September.
According to NGOs, the uptick reflected frustration among young people hard hit by unemployment.
In October, a collision between a migrant boat and a Tunisian military ship left at least 44 dead, in what Prime Minister Youssef Chahed called a "national disaster".