At least four bullets hit the door of the building, which was a former residence of a rabbi, the police said in a statement on Friday.
Officers were called to the building in the morning after witnesses saw the bullet holes in the door.
The building houses Steinheim Institute, whose research focuses on German-Jewish history.
It is next to the "Old Synagogue" of Essen, which is now a cultural institute, with exhibitions on Jewish history and culture.
Germany’s Jewish community has repeatedly warned that anti-Semitic incidents are again on the rise in the country and called for action.
Between January and September this year, German authorities registered more than 1,555 anti-Semitic incidents.
Source: Anadolu Agency