Yes, passengers arriving from a non-risk area can voluntarily and free of charge undergo testing at the coronavirus test center at the Forum of Munich Airport Center (MAC), level 04.
Departing passengers at Munich Airport have the opportunity to be tested for possible infection with the coronavirus SARS-CoV-2. The medical laboratory MVZ Martinsried offers such tests for a fee (128 euros) at the "Test & Fly" Center in Terminal 2, Level 04. The "Test & Fly" Center is open daily from 5 am to 7 pm. Outside the opening hours of the "Test&Fly" Center, departing passengers have the opportunity to undergo a PCR test via at Medicare, a subsidiary of Flughafen München GmbH, in the airport's medical center (Terminal 1, Module E, Level 03).