He added that the intelligence brigade chief and the Tunis district police chief, as well as the Bardo security chief, were among those dismissed.
On Saturday, Tunisian President Beji Caid Essebsi said in an interview with weekly news magazine Paris Match that "the police and intelligence services had not been thorough enough in protecting the museum."
On March 18, a group of gunmen, dressed in military uniform, opened fire at visitors to the National Bardo Museum. The country's security forces killed two terrorists after a two-hour standoff. The security forces are currently searching for a third attacker that fled the scene.
More than 20 people were killed and over 40 persons were wounded during the attack. Most of the victims were foreign tourists visiting the museum.
The Islamic State claimed responsibility for the attack on the museum.
According to the International Centre for the Study of Radicalisation and Political Violence, up to 3,000 Tunisians are among the estimated 20,000 foreign fighters who have joined Islamist militant groups in Iraq and Syria.