The three were detained in December 2013 in Cairo and later sentenced to up to 10 years in prison each, before Egypt's highest court ordered the retrial.
Judge Hassan Farid on Thursday ordered the postponement so defence lawyers would have a chance to deliver their closing arguments.
Fahmy, who was Al-Jazeera's Cairo acting bureau chief, Australian journalist Peter Greste and Egyptian producer Baher Mohammed are on retrial on charges of being part of a terrorist group and airing falsified footage intended to damage national security.
Greste was released and deported in February.
Fahmy, who has filed a civil lawsuit against Al Jazeera, and Mohammed were released on bail days later.Suggest a correction