The detainees include 10 who are believed to have been directly involved in the Bardo attack, according to Tunisian Interior Ministry spokesman Mohamed Ali Aroui.
"There is a large-scale campaign against the extremists," he said.
The Islamic State group claimed responsibility for the Wednesday attack on the museum, which is located next to the country's parliament.
The Saturday arrests came as hundreds of Tunisians gathered for a mass in the cathedral in central Tunis, lighting candles in memory of the victims of the attack.
The ceremony was attended by an array of senior government officials; police were on heightened alert outside the cathedral.
The Wednesday assault became the most deadly attack involving foreigners in Tunisia since the 2002 bombing of an ancient synagogue on the Tunisian island of Djerba.
