Young returned a positive test at the club’s training grounds on Saturday.
The 35-year-old Englishman is the sixth member of Antonio Conte’s side to test positive for the virus in the past week.
Defender Milan Skriniar tested positive for the virus while on international duty with Slovakia while the likes of Radja Nainggolan, Roberto Gagliardini, Alessandro Bastoni and goalkeeper Ionut Radu have all returned positive tests.
The club’s statement reads: “Inter announces that Ashley Young tested positive for Covid-19 following the test carried out yesterday [Saturday] in Appiano Gentile. The English footballer is already in quarantine at his home.”
Young, who has played in all three of Inter’s Serie A games this season, could now miss their next game against AC Milan next Saturday.
Young joined Inter from Manchester United in the January transfer window and played 18 times in Serie A, scoring four goals, as well featuring five times as the 2010 European Champions made the Europa League final, losing to Sevilla.
Inter Milan lie fourth on the Serie A table, having begun the season with two wins and a draw in their opening three games.
They have been drawn against Real Madrid, Borussia Monchengladbach and Shakhtar Donetsk in the UEFA Champions League group stages.