"Ashley Young tested positive for Covid-19 following the tests carried out yesterday (Saturday) at Appiano Gentile," the club said in a statement.
"The English player is already in quarantine at home."
Former Watform and Aston Villa player Young joined Inter from Manchester United in January.
The 35-year-old becomes the sixth player to test positive at the club after midfielders Radja Nainggolan and Roberto Gagliardini, defender Milan Skriniar, Italy under-21 international Alessandro Bastoni and goalkeeper Ionut Radu.
Serie A runners-up Inter Milan next meet city rivals AC Milan on October 17.
