Shaqiri, 28, was called up to the national team for the upcoming friendly against Croatia and UEFA Nations League clash in Spain.
After returning a positive test, Shaqiri is in isolation upon consultation of health authorities.
All three players missed Liverpool's stunning 7-2 defeat at the hands of Aston Villa on Sunday.
Liverpool boss Jurgen Klopp will be disappointed by the news after he warned that Premier League clubs were "left alone" regarding players leaving the country for international duty this week.
"In these moments as a club we are completely alone," he told a news conference on Friday.
"I know it's difficult. Here in our own country, TV broadcasters and the Premier League don't care. As a football club you are alone in this moment.
"We have to make sure we bring the players home in the quickest and safest way because nobody helps us. This is the situation we're in. It's really tricky. We try everything to make it right and as safe as possible."