Members of the U.S. forces, the civilian component and their dependants may be exempt under the NATO Status of Forces Agreement.
The exemption rests on Article 60 (5)(b) of the Supplementary Agreement. Your installation's legal office issues a confirmation letter, which goes to the Beitragsservice in Cologne.
Worth knowing: SOFA members are exempt from registering with the city at all, and it is usually a voluntary registration that triggers the fee demand in the first place.
Contact your installation's legal office for the confirmation letter.
If you are leaving, deal with this before you go — it is much harder from the United States.
Members of the U.S. forces, the civilian component and their dependants may be exempt under the NATO Status of Forces Agreement.