Nkunku suffered the injury in Chelsea's final game of their USA tour against Borussia Dortmund last week.
An update on the Chelsea website on Tuesday has revealed Nkunku will be out for an unspecified period of time.
"Nkunku has sustained a knee injury which will rule the forward out for an extended period," Chelsea said in a statement.
"The 25-year-old has undergone an operation and will now begin a rehabilitation programme with the club's medical department."
Nkunku joined Chelsea from RB Leipzig this summer and scored three times in five pre-season games for the Blues.
With Romelu Lukaku still out of the picture at Stamford Bridge, Chelsea manager Mauricio Pochettino only have summer signing Nicolas Jackson and Armando Broja as recognised centre forwards.
Chelsea start their season at home to Liverpool in the Premier League on Sunday.
