The two-time African footballer of the year has been in isolation in Egypt since Friday following the test that was carried out when he joined up with his global teammates.
Salah had also attended a ceremony organised by the Egyptian Football Association (EFA) in Cairo to celebrate his achievement of being the first Egyptian to win the Premier League and the Champions League.
The federation said he will undergo further checks in the coming hours.
It is also understood that the 28-year-old is not showing any symptoms.
Medical swabs on the national team "showed that our worldwide player, Mohamed Salah, Liverpool star, was infected with the coronavirus", it said in a tweet, adding he was "not suffering from any symptoms". "He has been isolated and the National Team's doctor is now liaising with Dr. Jim Moxon, head of Liverpool FC's medical staff, regarding this matter".
The Egyptian star is in high spirits and has not shown any typical symptoms.
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It is the latest major setback for Klopp in what is proving a particularly hard task in defending their Premier League title, having already lost defenders Virgil van Dijk and Joe Gomez to injury.
Gomez suffered a serious knee injury in England training on Wednesday and He underwent a "successful" surgery to blow a tendon with Liverpool hoping to make an appearance again this season.
Salah has been forced into quarantine while on worldwide duty after a positive coronavirus test.
The former Chelsea star is not considered the first worldwide star to contract the virus, after the captain of the Portugal national team Cristiano Ronaldo tested positive while he was with his country in October.
Salah, the Premier League's top scorer this season with eight goals, will have to isolate himself for ten days, to keep him out of the Leicester match next Saturday.
The EFA's statement added that the rest of the players tested negative for COVID-19 and they are ready for the match against Togo in the 2021 Africa Cup of Nations Qualifiers.