Nkunku, 25, joined the Blues in June from RB Leipzig for a reported £63 million.
The BBC and The Telegraph reported that Nkunku could be out for up to four months.
He was expected to spearhead a new-look Chelsea this season under the management of Mauricio Pochettino.
The news comes as a hammer blow just days before they begin their Premier League campaign at home to Liverpool on Sunday.
In a statement, Chelsea said: "Nkunku has sustained a knee injury which will rule the forward out for an extended period.
"The 25-year-old has undergone an operation and will now begin a rehabilitation programme with the club’s medical department."
Nkunku, who missed last year's World Cup finals due to a left knee problem, suffered the injury during a pre-season friendly against Borussia Dortmund in Chicago last week.
Pochettino described the pitch at Soldier Field as "not perfect" but conceded that is the risk in playing a money-spinning tour of the States on surfaces designed for multi-sport use.
Chelsea could now be forced into the transfer market to recruit more firepower.
A return of just 38 goals in the Premier League last season contributed to a 12th-placed finish - their lowest since 1994.
