Old English scamu, sceomu "feeling of guilt or disgrace; confusion caused by shame; disgrace, dishonor, insult, loss of esteem or reputation; shameful circumstance, what brings disgrace; modesty; private parts," from Proto-Germanic *skamo (cf. Old Saxon skama, Old Norse skömm, Swedish skam, Old Frisian scome, Dutch schaamte, Old High German scama, German Scham). The best guess is that this is from PIE *skem-, from *kem- "to cover" (covering oneself being a common expression of shame).
Until modern times English had a productive duplicate form in shand. An Old Norse word for it was