The story described is the myth of Actaeon and Artemis—but with a crucial correction: Actaeon did not recognize a loved one transformed into a deer; he himself was transformed.
Actaeon, a skilled hunter and grandson of Cadmus, accidentally stumbled upon the goddess Artemis bathing naked in a sacred forest spring. Enraged at being seen, Artemis splashed water on him, transforming him into a stag.
In his new form, Actaeon fled—only to be pursued and torn apart by his own hunting hounds (50+ dogs), who no longer recognized their master. He died in the woods, a victim of his own pack.
This myth appears in Ovid's Metamorphoses, Callimachus, and Euripides' lost play Actaeon. It has inspired countless artworks, from Titian to modern sculpture.