He scored in his side’s 3-1 victory over Arsenal on Monday but did not feature in the League Cup defeat by the Gunners three days later.
The club said the Senegalese star has displayed minor symptoms of the virus but “feels in good health overall.”
“I will begin my quarantine and recovery process immediately. Make sure that you stay safe and follow all rules to protect yourself and your loved ones, to avoid a second wave of the Covid-19.”
He has been nominated for the Premier League’s September player of the month award having scored three goals in three Liverpool victories.
Jurgen Klopp’s side next faces Aston Villa on Sunday.