Officers arrested the 28-year-old as he stepped out of a luxury villa on the island, which has a big German population, where he had been hiding, the police said in a statement.
The man, who was not identified, “remained the majority of the time hidden inside the villa to avoid being detected by Spanish police officers,” the statement added.
He is considered “very dangerous” by German authorities who suspect him of placing a homemade bomb in February in the German town of Burglengenfeld in the southern region of Bavaria.
The bomb, which included a vial of mercury to make it more powerful, was spotted by a local resident who alerted the authorities and it did not go off.
Police suspect the man is a member of the Reichsbürger (Citizens of the Reich) group, who do not recognize modern-day Germany as a legitimate state and insist the former, far larger Third Reich is still alive despite Nazi Germany's defeat in World War Two.
German authorities estimate that the Reichsbürger has around 20,000 members in Germany.