It alleged that four were directly linked to the attack and five had "ties to the cell".
The army will also be deployed to major cities, the presidency added.
In another development, Islamic State said in an audio message that it was behind the attack.
It said the attack was carried out by "two knights of the caliphate" and named them as Abu-Zakariya al-Tunisi and Abu-Anas al-Tunisi.
A statement described the attack as a "blessed invasion of one of the dens of infidels and vice in Muslim Tunisia".
The statement was published by Twitter accounts known to be reliable sources of IS propaganda.
One of two gunmen involved in the Bardo museum attack, named by Tunisian officials as Yassine Laabidi, was reportedly known to the authorities.
