Authorities in the state of Hesse say the man is suspected of planning a "serious state-endangering act of violence" and of violating German firearms laws. Investigations have been running for several months.
Police sought help identifying 22 women murdered in Germany, Belgium and the Netherlands whose names remain a mystery.
Almost a decade ago, 43 students went missing in southern Mexico while traveling by bus to the capital. The government alleges that a criminal gang killed them. So far, the remains of only three victims have been found.
Police have searched properties belonging to the Catholic Church's representative in Cologne amid accusations that Cardinal Rainer Maria Woelki covered up sexual abuse cases.
Police confirmed a trip to Germany by Ukraine's President Volodymyr Zelenskyy this month. But such plans are usually kept under wraps. One German outlet now cites Kyiv as saying it's furious and considering its options.
Interior Minister Nancy Faeser and the federal police are calling for more weapon-free zones on trains and in inner city areas in a bid to tackle knife crime.