According to the spokesman for Tunisia’s civil protection unit, Moez Triaa, the boat sank off the coast of Thyna near the port of Sfax in the morning.
A total of 20 Tunisians were on board the stricken boat, he said.
The body of one of them was retrieved from the sea while search operations are underway for six other passengers, Triaa added.
He said that authorities arrested 11 people who were aboard the vessel, while two others managed to escape.
Meanwhile, a spokesman for the National Guard told Mosaique FM, a private radio station, that its forces had arrested 223 people this week who tried to cross the Mediterranean illegally to Europe.
The migrants included 94 sub-Saharan Africans, the spokesman, Housemeddine Jebabli, said.
Thousands of young Tunisians make the often deadly sea crossing to Europe each year, driven by high unemployment at home.
According to Europe’s coast guard service Frontex, the number of illegal migrants trying to make their way to Europe fell by 85 per cent in April compared to the previous month.
Frontex linked the drop to the spread of the novel coronavirus pandemic.