Gundogan will undergo a 10-day period of self-isolation as per UK government and Premier League protocol.
In a statement, City said: "Manchester City FC can confirm that Ilkay Gundogan has tested positive for COVID-19.
"Ilkay is now observing a 10-day period of self-isolation in accordance with Premier League and UK Government protocol on quarantine.
“Everyone at the Club wishes Ilkay a speedy recovery.”
The 29-year-old German international is the third Manchester City player to test positive for coronavirus in recent weeks after Aymeric Laporte and Riyad Mahrez.
Both players have since recovered and while Mahrez will be available to face Wolverhampton Wanderers on Monday, Laporte is lacking match fitness and will sit out City’s opening Premier League game of the season.
Pep Guardiola’s side did not play in the opening weekend of the campaign after being granted an extended break following their exertions in the UEFA Champions League last month.
In addition to missing the game against Wolves on Monday, Gundogan will also be missing in action when the Cityzens come up against Bournemouth in the League Cup third round on Thursday as well as this weekend’s Premier League clash with Leicester City at the Etihad Stadium.
Gundogan made 50 appearances in all competitions for Manchester City last season, scoring five goals.