Quick answer: Munich Airport has NapCabs — private sleeping pods in Terminal 2 — bookable by the hour, with a bed, adjustable lighting, TV and free Wi-Fi.
NapCabs
Located airside in Terminal 2 (Level 4 near Gate 6, and Level 5 near Gate H32), NapCabs are compact private pods with a proper bed, relaxing music, TV, adjustable lighting and a small desk. You book and pay on-site by the hour with a credit card — useful for a long layover or an early-morning departure after a red-eye arrival.
Other rest options
If you'd rather not pay for a pod, the airport's lounges (see our lounges guide) offer quieter seating, and some travelers simply find a quieter gate-area bench — but a NapCab is the only option built specifically for sleeping.