BERLIN—Tesla is boosting factory worker pay in Germany amid an aggressive unionization drive, a move that comes as Chief Executive Elon Musk may face similar organizing attempts in the U.S.

Tesla’s management in Germany late last week unveiled a package of wage increases for workers during Musk’s visit to the so-called Gigafactory on the outskirts of Berlin, Tesla said on Monday. Musk also promised the assembly plant would build its next-generation vehicle.