Naguib Sawiris had been charged with insulting religion, but the billionaire was a no-show, said a judicial source.
The new hearing will be held February 11, Sherif Kamel said.
Sawiris spurred criticism after joking that Mickey and Minnie would be forced into conservative garb if Islamists took power.
The Coptic Christian businessman apologized for the caricature after Islamists urged a boycott of Mobinil, the cell phone service provider he owns. Even so, Islamist lawyer Mamduh Ismail filed a case against Sawiris, who heads Orascom Telecom.
Another lawyer, Ali Ahmad Borham, charged Saturday that the cartoon he tweeted was an “unprecedented” attempt in Egypt at making fun of religion, the source added.