The former-England captain sustained damaged knee ligaments during last month's draw with Liverpool after Luis Suarez accidentally landed on his right leg.
The European champions, who qualified for the Club World Cup by virtue of last season's Champions League triumph, had hoped the defender would be fit to take part in the upcoming competition.
But Chelsea boss Rafa Benitez confirmed his captain will not travel to Japan for the tournament.
"We've been talking with the doctor," said Benitez. "The inflammation during the flight will not be the best thing for him so he will not travel.
"He wanted to go and out to help, but it's better that he stays here. We don't know when he will play. We have to wait and see how he reacts."
The report claims Terry is yet to take part in full first-team training, so Benitez has decided not to take a chance with the 31-year-old's fitness.
Chelsea begin their quest for Club World Cup glory against either Mexican side Monterrey or Japanese outfit Ulsan Hyundai in Thursday's semi-final.
The Blues have never won the FIFA competition - the last English team to do so was Manchester United.