Al Ahly also said Tuesday they would also sell the 28-year-old at the end of the season and deprive him of prize money from the Cairo club's victory on Sunday in the final of the African Champions League.
Abdel Zaher held up four fingers when he scored the second goal in the 2-0 win over South Africa's Orlando Pirates.
The four-fingered salute has been adopted by supporters of Islamist former president Mohamed Morsi, who was overthrown by the army on July 3.
The player has apologised to fans for the political stunt, and said in a statement that he would be willing to accept whatever punishment the club metes out.
Al Ahly's football committee had on Monday recommended Abdel Zaher be suspended from next month's Fifa Club World Cup in Morocco, following uproar in the media.
Egypt remains deeply polarised between Morsi's supporters and the military-installed government, four months after his overthrow.
Following news of Abdel Zaher's suspension, several hundred supporters marched to his house in north Cairo in a show of solidarity..
Abdel Zaher appeared from a window to wave at his supporters and again flash the salute.
More than 1 000 people, mostly Islamists, have died in clashes since Morsi's overthrow, many of them killed when police dispersed a protest camp in Cairo's Rabaa al-Adawiya square.
The square is named after an eighth century Muslim holy woman, but Rabaa also means "fourth" in Arabic, giving rise to the four-finger salute Abdel Zaher flashed in the game.
An Egyptian martial artist, Mohamed Youssef, was banned from playing for two years after he wore a shirt bearing the symbol when he accepted his gold medal in a tournament in Russia last month. – Sapa