Greek mythology does feature a werewolf myth. Enjoy this deleted scene from a (very) early draft of Persephone to learn the full story behind werewolves.
Hestia leaned back, considering me with her fiery eyes. “Have you heard of the demigod Arcas, who killed the first werewolf–”
“Werewolf?” I sputtered.
“Zeus wished to add the muse Callisto to his list of conquests, however she was devoted to Artemis, and refused his advances. Zeus then disguised himself as Artemis, and seduced her.”
I raised my eyes at this information as Hestia continued, “Callisto was soon with child, and Artemis was enraged. Once the child was born, Artemis turned Callisto into a bear, and Zeus hid the child Arcas from Artemis.
He grew, and lived a relatively normal life until one day he got in trouble for stealing from King Lycaon. Once Lycaon discovered who he possessed in his dungeons, he tried to blackmail Zeus, threatening to kill Arcas unless Zeus blessed him with more wealth and power.”
I laughed, and she smiled at me, “Yes, not his brightest moment. Zeus cursed the king to become a werewolf, and allowed his son to have the honor of hunting down a beast with all the strength of a wolf and all the cunning of man–”
“The perfect game,” I muttered.
“Never mind,” I said waving my hand for her to continue.
“After a period of adjustment, Arcas hunted the King and successfully killed him, though he received a mortal wound in the process–”
“Did he have any kids? Pass down the curse?”
“Any children he created in human form remained human, and any children he created in wolf form were wolf.”
“Did he bite anyone?”
“That would not change them into a wolf. The only way to transform from human to animal is to be cursed by a god.”
“Oh.” I said disappointed.
Hestia smiled at me, “As Arcas lay dying in the woods, a large bear suddenly approached him–”
“Yes, the bear was his mother, as he drew back his bow to kill her, and when she realized he did not recognize her, despite her lingering in the shadows and watching him his entire life, she died of a broken heart. Zeus was horrified by their deaths, and in a rare moment of guilt memorialized them both in the stars as the constellations Ursa Major, and Ursa Minor.”