The man is described in the statement, published on Saxony’s police website, as being a "foreign person of southern type" in his 30s. He faces charges for disturbing peace by threatening to commit a criminal offense.
Police launched a large-scale operation to evacuate some 500 students to another school. The search for alleged explosives is still underway.
Germany has been on the edge since a series of truck, bomb and ax attacks by Islamists last year killed and wounded dozens. A failed asylum seeker from Tunisia rammed a truck into a Christmas market in Berlin last December killing 12 people.