COO Sheryl Sandberg, European policy director Richard Allan and Eva-Maria Kirschsieper, who heads the company's Berlin office, are all also under investigation, according to Spiegel.
Prosecutors confirmed the investigation to the Frankfurter Allgemeine Zeitung (FAZ) as well.
Investigators must prove whether there is enough evidence of a criminal offense and whether it would fall under the Munich prosecutors' jurisdiction.
The probe was initiated after a Bavarian lawyer reported the company to police, accusing its management of allowing racism, Holocaust denial and violent threats to remain on the site without consequence.
Facebook is legally bound in Germany to delete all known content which can be considered incitement of hatred.
The criminal complaint lists a series of postings which were reported to the company but were not deleted, with the complainant either being ignored or receiving a standard reply describing the post as “harmless” Spiegel reports.
A Facebook spokesman told FAZ that the company would "examine [the situation] calmly and if necessary respond with a statement".
A criminal complaint against Zuckerberg at the start of the year failed after prosecutors said that they could not investigate because the accused did not reside within the borders of the German justice system.
In October Volker Kauder, a key member of Chancellor Angela Merkel's party, said that social media giants like Facebook should face penalties if they fail to tackle hate speech, after a surge in xenophobic comments linked to the migrant influx.
“The time for round-tables is over. I've run out of patience," said Kauder, chairman of the Christian Democratic Union's parliamentary group.
Despite a pledge in December last year by Facebook, Twitter and Google to examine and remove offensive posts in Germany within 24 hours, users have reported that their requests to take down hate speech have often hit a wall.
Kauder said that if the companies fail to remove offensive posts within a week after they have been reported, then they should be penalized, with a suggested fine of €50,000 per post.
In an interview in October, Justice Minister Heiko Maas noted that the online giants had taken action only in a minority of cases.
Out of the cases reported to Twitter in Germany, only one percent was erased, he said, while for Facebook, the proportion was 46 percent.
"If the companies refuse to meet their responsibility, then there will be consequences," Maas told business daily Handelsblatt.