The club's television channel reported that Badri, who began his playing career with Al Ahli in the 1970s, quit along with his entire staff after a 3-1 loss to Ismaili left them in second place in the league, six points behind arch-rivals Zamalek.
Al Ahli said the board had not yet decided whether to accept his resignation.
Badri coached Al Ahli to their sixth successive league title last season but the club were knocked out of the African Champions League in October after losing to Tunisia's Esperance in the semi-finals.
Badri, the first Egyptian to coach the team since 1993, was handed the reins at the club last year after Portuguese Manuel Jose left to coach Angola's national team.
