The former United States coach led his team to a 2-1 win over Ghana on Tuesday, but they suffered a 7-3 aggregate loss after being handed an embarrassing loss in the first leg of their CAF World Cup qualifying tie.
Having spent just over two years at the helm, Bradley will be searching for a new job after Egypt missed out on a place at Brazil 2014.
"Bob Bradley's contract ended this night, and we will not renew for him, we will start search for a new coach," Egyptian Football Association chairman Gamal Allam said.
Bradley's men were hammered 6-1 in Ghana in the first leg, all but ending their chances of qualifying.
Allam said the American would have found it tough to remain as coach regardless after being criticised for the first-leg defeat.
"I think Bradley will not accept to stay here following all the criticism from the media after the first match in Kumasi. We did not talk with him about staying and we will not do so," he said.
"We won against Ghana but we did not qualify. We signed Bradley to take the team to the World Cup but he failed so we will search for new coach and we wish him good luck."
Allam said he planned to appoint an Egyptian coach, but was unwilling to say who was in his plans.
"We will sign an Egyptian coach," he said.
"But now I will not reveal who we have in mind but we will definitely not sign another foreign coach."
