late 15c., "interior, inward, internal," from Middle French intrinsèque "inner" (14c.), from Medieval Latin intrinsecus "interior, internal," from Latin intrinsecus (adv.) "inwardly, on the inside," from intra "within" (see intra-) + secus "along, alongside," from PIE *sekw-os- "following," suffixed form of root *sekw- (1) "to follow."
The form in English was conformed to words in -ic by 18c. Meaning "belonging to the nature of a thing" is from 1640s. Related: Intrinsical; intrinsically.