The former Athletic Bilbao midfielder sustained the injury to his left knee during the German Super Cup defeat to Borussia Dortmund.
However, after surgery and a lengthy rehabilitation programme, the Spaniard trained on Wednesday and is hopeful of featuring before the end of the season.
"It's just fantastic, I'm overjoyed," the 26-year-old told Bayern's official website.
"It's only the first step. I know I have a lot of work ahead of me yet.
"They [Bayern team-mates] were cheering and clapping for me. I guess they're all delighted for me. I hope I can pick up a few minutes playing time very soon."
Martinez arrived at the Allianz Arena in 2012 and was part of Jupp Heynckes' treble-winning side in his debut season.
Further honours followed under Pep Guardiola last term, including the Bundesliga title and the DFB-Pokal.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1
Get FourFourTwo Newsletter
The best features, fun and footballing quizzes, straight to your inbox every week.