The Frenchman will now undergo surgery after sustaining the injury in training last week.
"Yann has fractured his left ankle and will be operated on this week," Charlton physio Erol Umut told the club's official website.
"We were not happy with the outcome of his X-ray last Thursday after he had a collision in training and after Yann rested over the weekend, we had a further scan on Monday.
"That revealed the fracture, so he will be operated on this week, and it will potentially rule him out for three months."
Kermorgant had scored two goals in six games for the Addicks this season before he picked up his injury.