1560s, "sudden turn of mind," of unknown origin, perhaps related to Old English frician "to dance" (not recorded in Middle English, but the word may have survived in dialect) [OED, Barnhart], or perhaps from Middle English frek "bold, quickly," from Old English frec "greedy, gluttonous" (cf. German frech "bold, impudent").
Sense of "capricious notion" (1560s) and "unusual thing, fancy" (1784) preceded that of "strange or abnormal individual" (first in freak of nature, 1847; cf. Latin lusus naturæ, used in English from 1660s). The sense in health freak, ecology freak, etc. is attested from 1908 (originally Kodak freak, a camera buff). Freak show attested from 1887.