AS Roma player Mido will feature for the national team for the first time since February when he was handed a six-month suspension.
He was penalized after an angry exchange with manager Hassan Shehata on the touchline during Egypt's 2-1 win over Senegal in the African Cup semis.
Werder Bremen forward Zidan was also recalled after he missed Uruguay friendly earlier in August due to injury.
Zidan, who was dropped from the African Cup squad, shined in his side's preseason friendlies, prompting media and fans to demand his presence with the national team.
Five other European-based players were also recalled, with Egypt captain and Anderlecht holding midfielder Ahmed Hassan topping the list.
African champions Egypt host Burundi on September 2 in their first game in Group B of the qualifiers. The group also includes Mauritania and Botswana.
The Full Squad:
Goalkeepers: Essam Al-Hadari (Ahli), Mohamed Abdul-Monsef (Zamalek), Sherif Ekrami (Feyenoord/Holland).
Defenders: Abdul-Zaher Al-Saqqa (Konyaspor/Turkey), Amir Azmi (Paok/Greece), Ahmed Abou-Mosallam (Strasbourg/France), Wael Gomaa (Ahli), Ahmed Fathi, Hani Said (Ismaili).
Midfielders: Ahmed Hassan (Anderlecht/Belgium), Hosni Abd-Rabou (Ismaili), Reda Shehata (ENPPI), Ahmed Salem (Al-Gaish), Mohamed Abou-Treika, Mohamed Shawki (Ahli).
Forwards: Ahmed Hossam (Roma/Italy), Mohamed Zidan (Bremen/Germany), Emad Meteb (Ahli), Amr Zaki, Abdul-Halim Ali (Zamalek).