Animal rights group PETA protested last month after two horses were put down during filming of the show's second season.
An investigation is now ongoing following the death of a third animal, according to Deadline.
HBO has suspended the use of horses until the enquiry is complete. The most recent death occurred when one of the creatures flipped over backwards, striking its head on the ground.
Attending veterinarian Dr Heidi Agnic administered immediate aid to the injured horse and determined that humane euthanasia was the most appropriate course of action.
"An American Humane Association Certified Safety Representative was on the premises when the accident occurred, and as always, all safety precautions were in place," HBO said in a statement.
"HBO and everyone involved with the production are deeply saddened, and are working in full cooperation with the AHA and the California Horse Racing Board to complete their inquiry."
CHRB Equine Medical Director Dr Rick Arthur added: "Unfortunately, we see several of these injuries in the stable area every year. They are more common than people realise."
Filming on the second season of Luck continues at Santa Anita Race Track in the LA suburb of Arcadia.
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Watch a preview for the next episode of Luck below: