Is it possible to have any position in the executive branch without high school diploma? Are ministers required to have completed higher education degrees?
No, a specific level of education is no formal requirement for either the German Chancellor nor the Ministers. There are in fact almost no formal requirements for being elected as chancellor or being appointed as minister. Article 62 of the German Basic Law (constitution-equivalent) says the chancellor is whoever the parliament elects:
(1) The Federal Chancellor shall be elected by the Bundestag without debate on the proposal of the Federal President.
(2) The person who receives the votes of a majority of the Members of the Bundestag shall be elected. The person elected shall be appointed by the Federal President.
Curiously, Article 54, about the election of the German President, includes the following phrase:
Any German who is entitled to vote in Bundestag elections and has attained the age of forty may be elected.
while a similar phrase is lacking from Article 62. So theoretically not even citizenship, age or voting rights are required.
The appointment of Ministers is described in Article 64 which just says:
Federal Ministers shall be appointed and dismissed by the Federal President upon the proposal of the Federal Chancellor.
Again, no prerequisites at all. So the chancellor can propose whoever he/she wants, and the president will usually oblige (in theory... in practice the minister posts are handed out as bargain chips during the coalition negotiations).
The only limitation is Article 66, which says that the Chancellor and the Ministers must not have any other jobs:
Neither the Federal Chancellor nor a Federal Minister may hold any other salaried office, or engage in any trade or profession, or belong to the management or, without the consent of the Bundestag, to the supervisory board of an enterprise conducted for profit.
What about entry level positions in public administration?
There are four career progression paths in the German public administration with different educational prerequisites:
- "Einfacher Dienst" ("simple service") - requires a "Hauptschulabschluss", the lowest educational degree in the German school system
- "Mittlerer Dienst" ("medium service") - requires a vocational education
- "Gehobener Dienst" ("elevated service") - requires a bachelor-level college degree
- "Höherer Dienst" - ("higher service") requires a master-level college degree
Martin Schulz never went to college, but completed an apprenticeship as bookseller in 1977, so he would theoretically qualify for the "Mittlerer Dienst".