Salah had “a new swab to detect the Covid-19 virus, its result was positive”.
Arsenal player Mohamed Elneny was also re-tested and his result was also positive, the FA said.
Without Salah, Egypt beat Togo 3-1 in their 2021 Africa Cup of Nations qualifier on Tuesday and top their group.
Salah wrote on Twitter on Tuesday: “I’d like to thank everyone for the supportive messages and well wishes. I’m confident I’ll be back on the field soon.”
I’d like to thank everyone for the supportive messages and well wishes. I’m confident I’ll be back on the field soon 💪
— Mohamed Salah (@MoSalah) November 17, 2020
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The forward, who has scored eight league goals for Liverpool this season, could miss the Premier League champions’ next two matches.
They host Leicester in the league on Sunday before playing Italian side Atalanta in a Champions League tie at Anfield on 25 November.