Galloway has been vocal in his criticism of Egyptian authorities in recent days after their decision not to allow the about 200 vehicles in the convoy to arrive in Egypt through the port at Nuweiba.
The Egyptian foreign ministry later issued a statement saying Galloway would not be allowed to return to the country and accusing him of incitement over his criticism of the government.
Cairo insisted that the aid be sent back through Syria and then by ferry to the port of El-Arish on the Mediterranean.
Seven other members of the Viva Palestinian convoy have also been ordered arrested after being accused of inciting riots in El-Arish.
The decision by the attorney-general in North Sinai means the activists could be detained after passing through the Rafah border crossing from Gaza.
It was not clear if they were in Egyptian custody on Friday.
Late on Tuesday, more than 50 people were wounded during a clash between Egyptian authorities and international members of the convoy.
The protests were sparked by an Egyptian decision to allow 139 vehicles to enter Gaza through the Rafah crossing, but requiring a remaining 59 vehicles to pass via Israel.
Afterwards, clashes between Egyptian security forces and Palestinians waiting for the aid convoy led to the death of one Egyptian policeman.
Israel and Egypt have severely restricted travel to and from the Gaza Strip since Hamas seized power there in June 2007, after winning Palestinian legislative elections in 2006.
The blockade currently allows only very basic supplies into Gaza.
The siege has severely restricted essential supplies and placed Gazans in a dire situation, made worse by Israel's military assault last winter that reduced much of the territory to ruins.