c. 1200, from Old Norse skaða "to hurt, harm, damage, injure," from Proto-Germanic *skathan- (source also of Old English sceaþian "to hurt, injure," Old Saxon skathon, Old Frisian skethia, Middle Dutch scaden, Dutch schaden, Old High German scadon, German schaden, Gothic scaþjan "to injure, damage"), from PIE *sket- "to injure." Only cognate outside Germanic seems to be in Greek a-skethes "unharmed, unscathed."
It survives mostly in its negative form, unscathed, and in figurative meaning "sear with invective or satire" (1852, usually as scathing) which developed from the sense of "scar, scorch" used by Milton in "Paradise Lost" i.613 (1667).
"malicious joy in the misfortunes of others," 1922, German Schadenfreude, literally "damage-joy," from schaden "damage, harm, injury" (see scathe) + freude, from Old High German frewida "joy," from fro "happy," literally "hopping for joy," from Proto-Germanic *frawa- (see frolic).
What a fearful thing is it that any language should have a word expressive of the pleasure which men feel at the calamities of others; for the existence of the word bears testimony to the existence of the thing. And yet in more than one such a word is found. ... In the Greek epikhairekakia, in the German, 'Schadenfreude.' [Richard C. Trench, "On the Study of Words," 1852]
c. 1200, "to injure, wound" (the body, feelings, reputation, etc.), also "to stumble (into), bump into; charge against, rush, crash into; knock (things) together," from Old French hurter "to ram, strike, collide with" (Modern French heurter), a word of uncertain origin. Perhaps from Frankish *hurt "ram" (source also of Middle High German hurten "run at, collide," Old Norse hrutr "ram," Middle Dutch horten "to knock, dash against").
Celtic origins also have been proposed. The English usage is as old as the French, and perhaps there was a native Old English *hyrtan, but it has not been recorded.
Passive (intransitive) use "feel or experience pain" has been occasional in modern English; current usage dates from c. 1902. Meaning "to be a source of pain" (of a body part) is from 1850. Sense of "knock" died out 17c., but compare hurtle (v.). To hurt (one's) feelings attested by 1779. Other Germanic languages tend to use their form of English scathe in this sense (Danish skade, Swedish skada, German schaden, Dutch schaden).