Ghitani, 70, was originally admitted to El-Galaa military hospital after he faced difficulty in breathing.
"He died this morning," Ghitani's wife, Magda El-Gendi, told reporters.
His funeral will be held at Cairo's Sayyida Nafisa mosque later Sunday, state media reported.
Ghitani, a firm supporter of the army since the fall of veteran leader Hosni Mubarak in 2011, was one of Egypt's most acclaimed writers and shared a close friendship with the Arab world's only Nobel laureate, Naguib Mahfouz.
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"Gamal Ghitani contributed significantly in enriching literature with his unique style, intelligence and broad vision," Prime Minister Sharif Ismail said in a statement.
Ghitani's books, including widely praised novel Zayni Barakat, have been translated into several languages such as English, German and French.
An opponent of Islamists, Ghitani, who worked as a carpet designer before taking to writing, reported extensively from the frontline during the 1973 Arab-Israeli conflict.
Acclaimed locally and internationally, Ghitani won many awards, the latest being the Nile Award for Literature in 2015, the highest literary honour granted by the Egyptian government.
In 1987 he was made Chevalier de l'Ordre des Arts et des Lettres, a prestigious position awarded by the French government recognising significant achievement in the arts.
In 1993, Ghitani founded and headed Akhbar Al-Adab (Literature News), one of Egypt's literary newspapers, remaining its chief editor until 2011.