In his book "The Longest Struggle: Animal Advocacy from Pythagoras to Peta", Norm Phelps speaking about origins of animal protection refers to the times of Maurya Empire under Ashoka rules in 3rd century BCE, where it had mainly religious reasons. In his empire, not only hunting was banned, but also slaughter and eating of cattle, together with restrictions regarding fishing and fish-eating.
Norm Phelps describes it as "one of the very few instances in world history of a government treating its animals as citizens who are as deserving of its protection as the human residents".
In the medieval times, in the first half of 11th century there were regulations on fishing in Scotland, which covered some banned species and equipment. At the same time king of Poland, Boleslaw Chrobry banned the hunting of beavers at his land, as they were close to extinction.
But mainly, the reason for prohibition of hunting in medieval times were usually the property issues, as large areas of forests belonged to the crown of particular countries and through them, their vassals, what led to hunting monopoly of upper classes.