Maher was arrested Friday upon arriving from a trip abroad, The New York Times reported. He is accused of starting protests in front of the Interior Ministry in March.
After being arrested, Maher was transferred to a high-security prison where he will be held for four days pending an investigation into the accusations against him.
The April 6 official Twitter page called on supporters to show up at the airport to protest Maher's arrest, Ahram Online reported.
Mohamed Ibrahim, a member of the group's political arm, stated on Facebook that Maher has been "detained inside the airport with no legal justification."
However, an interior ministry official said Maher was taken into custody after the general prosecution issued a warrant for his arrest.
"Maher is accused of inciting protests in front of the residence of Interior Minister Mohamed Ibrahim," the official added.
Four other members of the April 6 group were arrested on March 29 and charged with rioting and resisting authorities following a protest held by the group at the residence of Ibrahim.