In 1912 he went to Munich and called on Wassily Kandinsky, the influential Russian painter and art theorist. Arp was encouraged by him in his researches and exhibited with the Der Blaue Reiter group. Later that year, he took part in a major exhibition in Zürich, along with Henri Matisse, Robert Delaunay, and Kandinsky. In Berlin in 1913, he was taken up by Herwarth Walden, the dealer and magazine editor who was at that time one of the most powerful figures in the European avant-garde. 

In 1915 he moved to Switzerland to take advantage of Swiss neutrality. Arp later told the story of how, when he was notified to report to the German consulate in Zürich, he pretended to be mentally ill in order to avoid being drafted into the German Army: after crossing himself whenever he saw a portrait of Paul von Hindenburg, Arp was given paperwork on which he was told to write his date of birth on the first blank line. Accordingly, he wrote "16/9/87"; he then wrote "16/9/87" on every other line as well, then drew one final line beneath them and, "without worrying too much about accuracy", calculated their sum.

Hans Richter, describing this story, noted that "they [the German authorities] believed him."

 In 1916 Hugo Ball opened the Cabaret Voltaire, which was to become the centre of Dada activities in Zürich for a group that included Arp, Marcel Janco, Tristan Tzara, and others. In 1920, as Hans Arp, along with Max Ernst and the social activist Alfred Grünwald, he set up the Cologne Dada group. In 1925 his work also appeared in the first exhibition of the Surrealist group at the Galérie Pierre in Paris.