Bassem Youssef has faced several complaints over his show Al Bernameg (The Programme).
The satirist has poked fun at a wide range of figures, from fellow television presenters to well-known Muslim scholars and recently Mohamed Morsi himself.
The case has highlighted worries about press freedoms in Egypt.
The move is also seen as the latest in a string of prosecution actions against opponents of the president and his party, the Muslim Brotherhood.
Earlier this week, Egypt’s top prosecutor ordered the arrest of five political activists, among them a leading blogger, on suspicion of inciting aggression against the Brotherhood.
The prosecutor, Talat Ibrahim, was appointed late last year by the president, after he had sacked his predecessor, Abdel Maguid Mahmoud.
However, a court this week ordered Maguid Mahmoud’s reinstatement, a decision that Talat Ibrahim said on Saturday he would fight.
Many journalists have criticized the Islamist-backed constitution which came into force earlier this year, arguing it does not offer enough guarantees for a free media.
The constitution also sparked protests from opponents who say it favors Islamists and does not sufficiently protect the rights of women or Christians.
Bassem Youssef is a doctor who shot to fame after winning a large number of followers with his witty lampooning of public figures in amateur videos posted on the internet following the uprising that ended Hosni Mubarak’s rule in February 2011.
He became a household name when his satirical show – likened to Jon Stewart’s The Daily Show in the US – began to be broadcast three times a week on one of Egypt’s independent satellite stations.
But sketches in which Bassem Youssef portrayed Mohamed Morsi as a pharaoh, calling him “Super Morsi” for holding on to executive and legislative powers, and, separately, putting the president’s image on a pillow and parodying his speeches angered one Islamist lawyer, whose formal complaint resulted in the investigation.
As well as insulting President Mohamed Morsi and Islam, Bassem Youssef is also accused of “spreading false news with the aim of disrupting public order”.
In a statement posted on Bassem Youssef’s Twitter account on Saturday he confirmed the warrant, adding: “I will go to the public prosecutor’s office on Sunday – unless they send me a police car and save me [the bother of] getting there on public transport.”
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