The news comes three days after the club said midfielder Thiago Alcantara had tested positive for Covid-19.
Liverpool say the Senegal winger has “displayed minor symptoms of the virus but feels in good health overall”.
Mane, 28, played for the Reds in a 3-1 win over Arsenal on Monday but was not in the squad for the EFL Cup defeat on penalties by the Gunners on Thursday.
A statement on Liverpool’s website added: “Like with Thiago Alcantara, Liverpool are – and will continue to – following all protocols relating to Covid-19 and Mane will self-isolate for the required period of time.”
Mane, who has scored three goals for the Anfield club this season, will miss the Premier League game against Aston Villa on Sunday prior to the international break.
The club’s first game after that will be the Merseyside derby at Everton on 17 October.
On Monday, the Premier League announced 10 people had tested positive for coronavirus in the latest round of testing – the highest number of positive tests since the season began.