The monument to the 17th Panzer Infantry Division, whose members are suspected of massacring 124 people in a village in central France in August 1944, was discovered in January in a field outside the northeastern village of Volmunster, on the border with Germany.
Set on private ground, the headstone was nonetheless visible to passers-by.
It read "In honour of the fallen of the 17th SS Panzergrenadier Division. Approach, Engage and Overrun!", according to pictures in French media.
Investigators working with the Office for Fighting Crimes against Humanity, Genocide and War Crimes seized the plaque and tracked down the owner of the field, a 34-year-old German living across the border in the Saarland region.
According to the local Republicain Lorrain newspaper, "various objects, as well as computer data", were seized during a search of his home in April.
German neo-Nazis have regularly congregated across the border in the Lorraine region of France, which together with neighbouring Alsace changed hands four times between France and Germany between 1870 and the end of World War II.
In 2012, authorities in Volmunster opposed renting out a local hall for a gathering of around 1,000 Neo-Nazis, mostly coming from Germany.
The gathering was held instead at a privately-owned hangar in Toul near the city of Nancy.
Several neo-Nazi "hatecore" rock concerts have also been held in the area.
French police say strict German laws banning Nazi symbols, even in private settings, have spurred white supremacists to continue their activities across the border.
In France, the police cannot break up a private party unless there is suspicion of criminal activity or a disturbance of the peace.