The 21-year-old picked up the problem during Borussia Dortmund's Champions League semi-final tie with Real Madrid in April, ruling him out of the final against his new employers Bayern.
And the injury turned out to be worse than first feared, meaning he has yet to join his new team-mates in full training.
However, he has now been given the green light by club doctor Hans-Wilhelm Muller-Wohlfahrt to step up his training regime, and Sammer says things are progressing well.
"Mario's right on track," he told the Bild newspaper. "He is getting excellent care from Dr Muller-Wohlfahrt and our physios.
"Mario is working like a true professional and is playing his part."
In spite of his progress, the Germany international is not expected to be ready for the German Super Cup against his former club later this month or the start of the Bundesliga campaign on August 9, when Bayern host Borussia Monchengladbach in Pep Guardiola's first competitive game in charge.