The 28-year-old Senegal international has displayed minor symptoms of the virus but is in good condition.
Mane was on target when Liverpool beat Arsenal 3-1 in the Premier League on Monday but missed out on the matchday squad against the same opposition in the Carabao Cup three days later.
The former Southampton forward will miss Sunday’s Premier League game against Aston Villa as a result.
Mane is the second Liverpool player to test positive for coronavirus this week after Thiago Alcantara.
"Sadio Mane has tested positive for Covid-19 and is currently self-isolating according to the necessary guidelines," the club said in a statement.
"The forward, who started and scored in Monday's 3-1 victory over Arsenal, has displayed minor symptoms of the virus but feels in good health overall.
"However, like with Thiago Alcantara, Liverpool Football Club are - and will continue to - follow all protocols relating to Covid-19 and Mane will self-isolate for the required period of time."
Mane will also miss Senegal’s upcoming friendly games against Morocco and Mauritania during the international break.
He has scored three goals in his opening three league games and has been named alongside Jamie Vardy, Harry Kane, Timothy Castagne, Tariq Lamptey, James Rodriguez, Dominic Calvert-Lewin and Patrick Bamford for September’s Premier League Player of the month.
