Staff at the Moritzburg nature reserve near Dresden, Saxony, found the 14-year-old stag's decapitated body on New Year's Day at 2pm.
Police said in a statement that they believe the culprits stole the animal's head as a hunting trophy and added the shooting breached animal protection laws.
Investigators called to the scene took samples from the corpse. It is thought to have been shot after sunset but no bullet hole has been found, meaning it was likely hit in the head.
Initial investigations revealed that the stag was shot just once and decapitated “unhuntsmanly and unprofessionally,” head of the area's forest authority Markus Biernath told the regional Säschsiche Zeitung on Tuesday.
This limit the chances of it being sold, police said, and would make it easier to identify if the head were to turn up.
Biernath called the death a “huge loss.” The white stag lived alongside 30 other rare species in the 40 hectare reserve, like lynxes and elks.
White deers have a condition called leucism that causes skin and hair to lose colour, thus making them very rare.