My Pet Monster is a direct-to-video live-action special released in 1986.
Storyline
A boy named Max and his sister Melanie go to a museum and see a monster-like statue that Dr. Snyder had brought back from the Middle East. After being exposed to the statue and sunlight simultaneously, Max finds himself turning into a furry blue monster whenever he gets hungry. Dr. Snyder tries to hold him captive, but Max escapes and eludes him.