The 32-year-old has "been released early from international duty amid the ongoing October break," Liverpool said.
On Friday, Salah scored for Egypt in a 2-0 victory over Mauritania and had been due to play a second fixture against the same opponents on Tuesday.
Egypt manager Hossam Hassan had told journalists in Cairo on Friday that there were concerns over playing on Mauritania's artificial turf and injury fears.
Record seven-time African champions Egypt faced stubborn resistance from Mauritania until Mahmoud 'Trezeguet' Hassan netted 69 minutes into the Group C clash.
Prolific Liverpool scorer Salah put the outcome beyond doubt with a second goal 10 minutes later to maintain the perfect record of the Pharaohs after three rounds.
Egypt need a single point in the next match to qualify as they sit six points ahead of rivals Cape Verde, Botswana and Mauritania.
Liverpool also confirmed that Dutch defender Virgil van Dijk had been also released early from international duty.
Van Dijk was dismissed for the Netherlands after picking up two yellow cards during a 1-1 UEFA Nations League draw with Hungary.
"The pair will take no further part for their respective nations this month after the decision was made to relieve them both early from their international commitments."
