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 Muller-Wohlfahrt.
"Luckily it is a capsule strain," Muller-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 amid heavy snowfall.
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 January 19.
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