The disclosure provides a new and distinct hybrid melon variety NUN 68956 MEM as well as seeds and plants and fruits thereof. NUN 68956 MEM is a small Piel de Sapo melon variety comprising resistance to Melon Yellowing Associated Virus (MYaV), Fusarium oxysporum f.sp. melonis Race 0 and Race 1, and Podosphaera xanthii Race 1 and Race 2.