Reigning champions Bayern progressed to the quarter-finals with a 3-1 aggregate victory, but two banners displayed by home fans at the Allianz Arena could land the club in hot water.
One crudely made banner depicted a man in an Arsenal away strip bent over in front of a cannon and was emblazoned with the words "Gay Gunners", while another read "Say no to racism, say yes to Kosovo" in reference to a campaign to have the territory officially recognised by FIFA.
The European governing body are also looking into the late kick-off of Tuesday's second leg clash.
In a statement, UEFA said: "Disciplinary proceedings have been opened against FC Bayern Munchen for discriminatory behaviour of their supporters (art. 14 DR), display of an illicit banner (art. 16 (2) (e) DR), and late kick-off (art. 11 (2) (g) DR) at their UEFA Champions League round of 16 match against Arsenal FC (1-1), which was played in Germany on Tuesday.
"The case will be dealt with by the UEFA Control and Disciplinary Body on 20 March."
Celtic were fined €50,000 in December for the display of "illicit" banners in their home tie with Milan.
Ajax were also fined €10,000 by UEFA last season for displaying a banner referencing Manchester City's ownership when facing the Premier League club.
