The 27-year-old Salah had already been called up for the first match under El-Badry alongside four other foreign-based players.
"Mohamed Salah has been suffering from fatigue due to the games sequence so he won't be included in the team's training camp when we play the friendly against Botswana," El-Badry said on television.
"Salah is suffering from muscle fatigue. He's been given medicines by the club's medical staff and he needs to rest," the 59-year-old former Ahly coach added.
However, "Salah will join the Egypt national team squad in the Africa Cup of Nations qualifiers," El-Badry added.
Salah, the top scorer in the Premier League for the past two seasons, made a fine start to the new campaign with Liverpool, netting four goals in the opening seven matches as the Reds top the table with a maximum 21 points.
El-Badry is the first Egyptian manager in the coaching hot seat in four years following Argentinean tactician Hector Cuper (2015-2018) and Javier Aguirre (2018-2019).
Egypt are competing in the 2021 Africa Cup of Nations qualifiers alongside the 2022 World Cup qualifiers.
The team has not played since its exit from the African Cup of Nations last July, which was held in Egypt.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)