Starting 27 November 2020, federal invoice issuers are obliged to submit their invoices electronically in accordance with Section 3 E-RechV. You can read about exceptions to this regulation in the FAQ section on e-invoicing.
In the German federal states, electronic invoice exchange is regulated independently: The corresponding implementation acts define when an acceptance obligation for public authorities exists and whether suppliers/service providers have an invoicing obligation. Enquiries in this regard should be directed to the competent federal state authorities.
KoSIT summarises the implementation status of the German federal states and makes it available.