Youssef is also accused of promoting atheism and insulting the attorney general, officials said.
The former heart surgeon hosts the popular weekly show "Al-Barnameg" and is known as Egypt's Jon Stewart, of "The Daily Show" fame.
Ahram Online said the investigation stems from comments Youssef made on his show.
In March, he mocked President Mohamed Morsi's speech at a Pakistani university, and 12 people filed complaints following the episode, Ahram Online said.
He has also allegedly made negative comments about religious obligations and, therefore promoted atheism, critics of the comic said.
Youssef is also accused of mocking the attorney general while he was at the prosecutor general's office.
Prosecutors questioned Youssef on March 31 and then released him on bail, Ahram Online said.