Martinez, who joined Bayern from Athletic Bilbao in the close season for a German record fee of 40 million euros but has yet to live up to his price tag, underwent treatment at the clinic of team doctor Hans-Wilhelm Mueller-Wohlfahrt.
"Luckily it is a capsule strain," Mueller-Wohlfahrt said of Martinez's ankle injury.
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.
Martinez is expected to join team training again on Thursday and be ready for Friday's last game of the year.
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.
