This question has at least three sides, so better read it as a whole:
First, from an business point of view the manager is probably right when he does not want his team to consist of people of a single nationality, especially if that's not German. I have seen this and there is a very real risk of such a team drifting apart from the rest of the company because they won't even try to get into German customs and following German rules. Prime examples would be eastern European programmers, who would comment their code in Cyrillic letters (probably Russian) despite company guideline to use English, so that their work output is basically worthless to anyone but them. A company cannot take such a risk.
Legally, discrimination based on something the person cannot change is forbidden. The relevant law is called the Allgemeines Gleichbehandlungsgesetz (translated: Common Law of treating all people equal). Relevant §§.
Ziel des Gesetzes ist, Benachteiligungen aus Gründen der Rasse oder wegen der ethnischen Herkunft, des Geschlechts, der Religion oder Weltanschauung, einer Behinderung, des Alters oder der sexuellen Identität zu verhindern oder zu beseitigen.
The aim of this law is to remove or hinder the discrimination based on race, ethnic background, gender, religion or world view, a disability, age or sexual identity.
Please note that Nationality is not one of them. Only ethnic background. So by the letter of the law, "I don't hire arabs." would be discrimination, "I don't hire Egyptians." would be fine. Although separating one from the other probably takes a court.
There are exceptions to the law though. Positive discrimination does exist and is legal. You will often find sentences like this
Bei gleicher Eignung werden Frauen und Behinderte bevorzugt
Technical skills being equal, women and disabled people will be preferred.
As most of the workforce in Germany is dominated by white males, going for more diversity is allowed and even enforced by unions and civil administration. So I am no lawyer, but if your team already consists of X people of the same trait, looking for one who is different does have indeed a precedent with women and disabled people.
Conclusion: To actually get a solid answer, you'd need a very specialized lawyer. But from just reading the laws, the statement of your boss seems borderline, but ok. There is precedent for exceptions and it actually makes sense (as opposed to a general "no blacks" or "no women"). However, it's laws. Much depends on how good your lawyer is at twisting and bending the laws to his will.