The Tunis public prosecutor said Saturday the arrest was in line with Tunisian law, and rejected the brothers' request to lift a travel ban and asset freeze.
A senior member of Karoui's Heart of Tunisia party, Iyadh Elloumi, said Saturday that he's a "political prisoner" and accused Prime Minister Youssef Chahed and his family of plotting against the tycoon.
Chahed is also a leading candidate in the elections.
Karoui's party said it is worried about the businessman's health and safety and called on the acting president to release him. In a statement, it called the arrest a "fascist" move reminiscent of actions under former autocratic President Zine El Abidine Ben Ali, overthrown in a 2011 revolution.
Tunisia unleashed the Arab Spring uprisings in 2011 and is the only country to emerge with a functioning democracy, but its leaders have failed to boost the economy or prevent Islamic extremist attacks.
Tunisia's justice minister ordered an investigation into the circumstances of the arrest to ensure it is according to regulation, according to Radio Mosaique.
The head of once-powerful Islamist party Ennahdha, Rached Ghannouchi, was among other politicians who have weighed in. He said at a rally Friday: "We are not happy about this arrest or the disruption of the activities of any party or political leader."