"Tunisian authorities have asked for his extradition," ministry spokesman Mohammed Ali Aroui told AFP.
He said Abdel Majid Touil, arrested in Italy on Tuesday, was suspected of having provided "logistical support" for the March 18th attack in which 21 tourists and a policeman were gunned down.
Italian police said Touil, 22, had been in Italy before the attack. They said he entered illegally in February with a boatload of migrants.
Tunisian authorities say international arrest warrants have also been issued for an Algerian and a second Moroccan over the Bardo killings.
At least 23 people have been arrested in Tunisia in connection with the attack which was claimed by the Islamic State jihadist group