The EFA officially condemned the duo's behavior as they announced on Saturday that the former Egypt internationals will be summoned to an investigation.
"The FA board decided to ban Hossam Hassan and Ibrahim Hassan indefinitely and summon the duo to an investigation for their irresponsible acts in the match against Bejaia," a statement by the Egyptian FA read.
"The decision comes in accordance with the FA's concern to maintain the friendly relationship with Algerian football."
The FA will take further action upon receiving the match report from Moroccan referee Khaled Ramses.
Coach Hossam Hassan, who was subjected to several disciplinary actions this season, was sent off for protesting during the North African Cup Winners Cup semi-final in Algeria.
However, it was Hassan's brother Ibrahim (football director), who caused further havoc after the game when he spat at the referee, assaulted the fourth official and made improper gestures towards the home crowd.
The Hassan twins' acts could add more tension to the crunch double-header between Egypt and Algeria in the 2010 World Cup qualifiers next year.