The 29-year-old, who joined from Bayern Munich this month, missed Monday’s 3-1 win over Arsenal and will now self-isolate.
“Thiago Alcantara has tested positive for Covid-19 and is currently self-isolating according to the necessary guidelines,” Liverpool said in a statement.
“The club has, and will continue to follow, all protocols relating to Covid-19 and Thiago will remain in self-isolation for the required period of time.”
The Spanish international will miss another clash with Arsenal in the League Cup on Thursday aswell as Sunday’s Premier League trip to Aston Villa, but could be available for the Merseyside derby at Everton on October 17.
On Monday, the Premier League announced 10 players or staff had tested positive for COVID-19 in the previous week, the highest number of infections since mass testing began in May.