The meeting, which took place in Munich, ended with a score of 3: 2 in favor of the guests.
PSG took the lead in the 3rd minute thanks to a goal by Kylian Mbappé.
Marquinhos doubled his team's lead in the 28th minute.
Bayern responded with goals from Eric Chupo-Moting, who scored in the 37th minute, and Thomas Müller, who scored in the 60th minute.
The winning goal for PSG was scored by Mbappé in the 68th minute, thus making a double.
The return leg will take place in Paris on April 13th.
Earlier it was reported that Chelsea beat Porto in the first leg of the Champions League quarter-finals.