The incident occurred Monday night when shots were fired from a passing car at Badr, the Arab news network said. Badr was not hurt in the attack. The movement submitted a complaint to police.
Badr was returning home after attending a session to review Egypt's draft constitution. Death threats had already forced him to change his residence to an unknown location, al-Arabiya said.
The attack came less than a week after Egyptian Interior Minister Mohammed Ibrahim survived an assassination attempt. The Ansar Beit al-Magdes claimed responsibility for detonating a bomb near Ibrahim's convoy last Thursday, al-Masry al-Youm said.
The group also warned Egyptian citizens to stay away from Defense and Interior ministry installations, saying the attack on Ibrahim was to avenge attacks of the Republican Guard Rabaa al-Adweya, Ramses and Alexandria, the Egyptian newspaper said.
Tamarod, an Egyptian grassroots movement, was founded to register opposition to Morsi and collected about 15 million signatures to support their demands that he resign. It helped wage the protests that led to Morsi's removal from office by the military in July.