The animal's head was placed in the middle of a Star of David on the entrance gate to the graveyard in Gotha near Erfurt and blood-red liquid and broken glass had been thrown at the gate.
The six million figure refers to the number of Jews killed by the Nazis. The pig's head was discovered on Monday morning. Police said they were investigating.
Earlier this month Germany marked with solemn ceremonies the 70th anniversary of the Kristallnacht pogrom when Jewish shop fronts were smashed, synagogues set on fire and Jewish men rounded up in 1938 in what historians call a prelude to the Holocaust.