"The prosecutor has decided to place in detention" satirist Migalo, whose real name is Wassim Lahrissi, and television host Moez Ben Gharbia for having "offended the president", prosecution spokesman Sofiene Sliti said.
He declined to give further details on the alleged offence, but alleged that the pair had also committed "fraud" and said they will remain behind bars until they appear in court on March 25.
The arrests came after Essebsi won Tunisia's first free presidential election in December, capping off the transition to democracy in the birthplace of the Arab Spring.
"We will not enter into the details of the case," so as not to undermine the investigation, Sliti said.
Private radio station Mosaique FM, where Migalo works as a comedian and impersonator, said that he had recently pretended to be the Tunisian president in a telephone call he made to a businessman.
According to the broadcaster, the businessman, whom they did not name, had recently asked Ben Gharbia to intercede on his behalf with the president but did not say what it was about.
There was no immediate comment from the office of the president, who has pledged to respect freedom of expression, which has been one of the main gains of the 2011 revolt that ousted veteran strongman Zine El Abidine Ben Ali.
The arrests came days after a Tunisian military appeals court jailed blogger Yassine Ayari for six months for defaming the army, despite criticism from rights groups.
Ayari has alleged that he is being punished for blogs he wrote while out of the country that were critical of Essebsi's anti-Islamist Nidaa Tounes party.
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