Official measures in the context of the corona pandemic can usually be issued by the local police or the responsible health authority, depending on the specific regulations of the federal states. Particularly important with regard to operational pandemic protection are the provisions of Sections 30, 31 IfSG (Infektionsschutzgesetz ─ German Infection Protection Act), which regulate the quarantine order and the prohibition of professional activity by the public health department, as well as the general clauses in Section 16 (1) and (2) sentence 3 IfSG (for these, please see the next question). The legal basis, which can be enquired from the respective authority, depends on the specific official request.
In case of requests from competent authorities, for example concerning ill employees, it must be assumed that the employer has a corresponding authorisation for the transmission of the requested information.
Source: The Baden-Württemberg State Commissioner for Data Protection and Freedom of Information (available at https://www.baden-wuerttemberg.datenschutz.de/faq-corona/) (in German)