Because he was born to a Jewish mother, which is the definition Jews use. Her name was Pauline Einstein, née Koch; the Einsteins were Ashkenazi Jews from Ulm. And of course, Einstein himself always considered himself to be Jewish, even though he did not practice the religion.
Naturally, the Nazis also considered him Jewish, which was their main argument against his physics; however, their main argument against Einstein personally was that he was a noted pacifist. This was if anything, worse in their eyes: even the Nazis understood that Einstein couldn’t help being Jewish, while pacifism was an active choice on his part.