Martinez, who joined Bayern from Athletic Bilbao in the close season for a German record fee of 40 million euros ($51.70 million) but has yet to live up to his price tag, will undergo more tests at the clinic of team doctor Hans-Wilhelm Mueller-Wohlfahrt later on Tuesday.
The Spain international, who has only recently won a starting spot in the team and has said he is still not at 100 percent after a busy last season for club and country, clashed with Boateng on a snow-covered pitch amid heavy snowfall.
Bayern have opened up an 11-point lead at the top of the Bundesliga following a record-breaking start to the season and have also advanced to the knockout stage of the Champions League.
The Bundesliga will break after this week's matches for just over a month and will resume on Jan 19. ($1 = 0.7736 euros) (Reporting by Karolos Grohmann; Editing by Julien Pretot)