The 18-year-old explained the situation in an interview with the club's own media.
"Time is tight before pre-season training begins on 20 July," Karl said. "It will still take a while before I can join in with the sessions with the boys. Right now, the most important thing is not to rush anything.
"I am in contact with the doctors and fitness coaches every day, and we are watching very closely how the muscle is responding."
Karl suffered a torn muscle fibre in his left thigh while training with the national team ahead of the World Cup, an injury that ruled him out of the tournament entirely.
The midfielder began building his fitness back up at the start of this week.
"For me, it means cycling and careful jogging for now, everything still very measured," Karl said. "Only after that will it move on to the pitch, with running work and the first exercises with the ball."
According to Bild, the German record champions are planning for their young talent to be out for at least eight more weeks, a significant blow given the excitement generated by his rise through the ranks over the past year.
That timeline would mean Karl misses the start of Bayern Munich's pre-season schedule and potentially the opening weeks of the new Bundesliga campaign, should the recovery process not accelerate.
Karl's setback comes after a breakthrough campaign at Bayern, in which he became the youngest player in Champions League history to score in three consecutive matches in the competition.
The 18-year-old also earned his senior Germany debut during the season, making his absence from the national team's World Cup squad all the more disappointing for player and club alike.
Bayern will be cautious not to rush his return given his age and the long-term importance he is expected to hold for the club in the coming seasons.