The negative wording is the key.
Pay attention to the word not in the question. Three of the proposed portfolios belong to the state government. Foreign Minister, however, is not a Niedersachsen ministerial office. The current government overview confirms that distinction.
Article 32 of the Basic Law states that maintaining relations with foreign states is a federal responsibility. This does not prohibit all international contacts by federal states. Niedersachsen has European and cross-border cooperation among its responsibilities.

The other three answers
These three portfolios exist at state level.
Justice Minister
Niedersachsen has a justice portfolio. It is therefore not the absent office asked for. Justice administration does not mean directing judicial decisions.
Finance Minister
A finance portfolio belongs to the state government and handles state finances. The federation also managing finances does not remove this state responsibility.
Interior Minister
An interior portfolio also belongs to Niedersachsen’s government. Responsibilities within the state are distinct from Germany’s foreign relations.
International cooperation remains possible.
Under Article 32, states may also conclude treaties with foreign states in areas within their legislative competence, with the federal government’s consent. The rule is therefore more precise than “states may never act externally”. Niedersachsen’s constitution also regulates the state’s external representation.
A portfolio for Europe or regional cooperation is not the same as a foreign ministry. Likewise, a justice ministry may administer courts, but may not tell independent judges how to decide a particular case. Responsibilities and legal limits belong together.
Article 32 · Foreign relations · Basic Law and state government ↗The question asks “not”: Foreign Minister.
International contacts are possible; a separate foreign-minister office does not exist.
Three words for this question
- das Außenministeriumforeign ministry
- The department responsible for a country’s relations with other states.
- grenzüberschreitendcross-border
- Extending across a national or regional border.
- die Zuständigkeitresponsibility / competence
- The area of work legally assigned to a body.
