Old English scamu, sceomu "painful feeling of guilt or disgrace; confusion caused by shame; state of being in disgrace; dishonor, insult, loss of esteem or reputation; shameful circumstance, what brings disgrace; modesty," from Proto-Germanic *skamo (source also of Old Saxon skama, Old Norse skömm, Swedish skam, Old Frisian scome, Dutch schaamte, Old High German scama, German Scham), which is of unknown etymology. The best guess is that this is from PIE *skem-, from *kem- "to cover" (covering oneself being a common expression of shame).
It is attested by c. 1300 as "modesty, shyness, regard for propriety or decency;" by 1580s as "thing or person to be ashamed of." To put (someone or something) to shame "inflict disgrace or dishonor upon" is mid-13c. Shame culture attested by 1947. The interjection for shame! "you should be ashamed" is by c. 1300.
Also in Middle English "nakedness, private parts, the genitals," as in the Wycliffite Bible's shameful thingis for Latin verecundiora. and shamfast membris for the male genitalia.
Until modern times English had a productive duplicate form in shand. 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" (aiskhynē) from shame in the good sense of "modesty, bashfulness" (aidos).