Sclerocactus wrightiae is a rare species of cactus known by the common names Wright's little barrel cactus and Wright's fishhook cactus. Dr. Lyman Benson named this species for North American cactus expert Dorde Wright Woodruff, who initially discovered it in 1961 and brought it to the attention of Dr. Benson. Dr. Benson and Ms. Woodruff later collaborated in connection with other Sclerocactus taxa in the Intermountain West.