The 24-year-old centre-back had to be replaced just before half-time in the Champions League match against Shakhtar Donetsk at Celtic Park on Wednesday night, leaving the pitch on a stretcher after an awkward fall.
There was immediate concern that Kennedy might have suffered a recurrence of the serious injury to his left knee, which kept him out of the game for three years until his return at the end of last season.
However, Celtic declared last night on their website: "John Kennedy today underwent an MRI scan on his left knee. Initial results show that John has sustained damage to his lateral meniscus and the posterior lateral complex of the knee, which could mean the injury isn't as severe as first thought.
"An arthroscopic investigation will be carried out on John's knee tomorrow morning and will confirm the extent of the damage. If the initial diagnosis is confirmed, John could possibly return to action within 12 weeks."