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]