Hesham Zazou said that following the appointment of Adel al-Khayat -- a member of the political arm of ex-Islamic militant group Gamaa Islamiya-- he "cannot continue in his role as minister of tourism."
Khayat's nomination sparked fury across the tourism sector, a once-lucrative industry which has been devastated in the aftermath of the 2011 uprising that toppled Hosni Mubarak.
Prime Minister Hesham Qandil has refused Zazou's resignation and asked him to remain in his post until the situation is reviewed, ministry spokeswoman Rasha al-Azaizy told the official MENA news agency.
Khayat belongs to the Construction and Development party, the political arm of Gamaa Islamiya which was blamed for a spate of attacks in the 1990s before it renounced violence.
Gamaa Islamiya claimed responsibility for an attack on a major tourist attraction in Luxor, in southern Egypt, that killed 58 foreign holidaymakers in 1997.