The midfielder limped off the pitch after being on the receiving end of a challenge from Tottenham’s Ben Davies during Sunday night’s 1-1 draw with Wales.
He was replaced by Luka Modric after failing to return to the pitch for the second half, adding another international concern for Blues boss Frank Lampard.
N’Golo Kante suffered a groin injury in the warm-up to France’s Euro 2020 qualifier on Friday, the Evening Standard reports.
That came on the back of Reece James and Trevor Chalobah’s withdrawals from the England Under-21 squad last week because of concerns over their match fitness.
To make matters worse, defender Andreas Christensen had to be replaced during Denmark’s 1-0 victory over Switzerland on Saturday with a groin problem.
Even on-loan Chelsea player Ethan Ampadu, who is spending this season at RB Leipzig, was taken off and required treatment after being on the receiving end of a robust challenge while starring for Wales.
The Blues’ injury list already includes Ruben Loftus-Cheek, Antonio Rudiger and Emerson Palmieri.
Lampard’s side host Newcastle United when they return to Premier League action at Stamford Bridge on Saturday, before a trip to Ajax in the Champions League the following week.
Kovacic, whose loan move from Real Madrid was made permanent over the summer, has been an important figure for the new boss so far this season and featured in every league game so far.
Chelsea are currently fifth in the league on 14 points, two behind second-placed Manchester City but 10 adrift of runaway leaders Liverpool.
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