The present subject matter provides a damper valve. The damper valve includes an outer sleeve and an inner sleeve. The inner sleeve is positioned within the outer sleeve and is pivotable between a first position and a second position within the outer sleeve. Radial openings of the inner sleeve align with radial openings of the outer sleeve when the inner sleeve is in the first position, and axial openings of the inner sleeve align with axial openings of the outer sleeve when the inner sleeve is in the second position. A related heat pump water heater appliance is also provided.