1670s, "offensive to a refined sense of propriety, beyond the bounds of proper reserve," from in- (1) "not, opposite of" + delicate. Related: Indelicately.
Immorality and indelicacy are different things. Rabelais is indelicate to the last degree, but he is not really immoral. Congreve is far less indelicate, but far more immoral. [James Hadley, "Essays Philological and Critical," 1873]