Old English sceamu, sceomu "feeling of guilt or disgrace," from Proto-Germanic *skamo (cf. Old Saxon skama, Old Norse skömm, Swedish skam, Old Frisian scome, Dutch schaamte, Old High German scama, German Scham), probably from PIE *skem-, from *kem- "to cover" (covering oneself being a common expression of shame).
An Old Norse word for it was kinnroði, literally "cheek-redness," hence, "blush of shame." Greek distinguished shame in the bad sense of "disgrace, dishonor" (aiskhyne) from shame in the good sense of "modesty, bashfulness" (aidos).