The governing body said a medical swab taken from the 28-year-old came back positive for Covid-19, but said the player was not suffering from any symptoms.
Liverpool are not due to play again until their home Premier League match against Leicester on November 21 and then at Brighton on November 28.
The news comes a day after it was confirmed Reds defender Joe Gomez had undergone knee surgery following an injury suffered in England training.
Salah’s positive test comes after he reportedly attended his brother’s wedding, with footage posted on social media appearing to show him dancing with other guests.
The EFA said Salah was now isolating, and that he would be “subject to more checks in the coming hours”.
The positive test should not sideline him for too long, provided he remains asymptomatic or develops only mild symptoms.
Gomez is set for a lengthier spell on the sidelines.
Liverpool said he had damaged a tendon in his left knee but there was no ligament damage.
Virgil Van Dijk has suffered a long-term knee injury while Fabinho is also sidelined.
England full-back Trent Alexander-Arnold is set to be out for around four weeks after injuring his calf in Liverpool’s draw with Manchester City last Sunday.