Hassan, 60, renewed his contract until 2030 after leading Egypt to the round of 16 at this year's World Cup, but the EFA said the decision followed a review of recent events.
"The Egyptian FA thanked Hossam Hassan for his efforts during his time in charge and wished him success in the next stage of his career. The board also appointed Ali Maher as head coach of the national team for the coming period," it said in a statement.
Egypt secured their first World Cup win against New Zealand under Hassan before beating Australia on penalties in the round of 32, but squandered a lead to lose 3-2 to Argentina in the last 16.
A 0-0 home draw with Angola in a Nations Cup qualifier in September came under scrutiny, however, after Hassan substituted talisman Mohamed Salah in the 60th minute.
The Trabzonspor forward left the national team camp, with the EFA saying he avoids playing on artificial pitches and would therefore miss the match against South Sudan.
EFA President Hany Abo Rida flew to Turkey this month to meet Salah.
Maher, 52, will take charge of Egypt after a successful spell with Ceramica Cleopatra.
Hassan, who received a three-match ban from FIFA after criticising the referee following Egypt’s defeat by Argentina, left the national team after 38 matches in charge, winning 21, drawing 10 and losing seven.
Egypt face Malawi twice this month in Africa Cup of Nations qualifiers.