mid-15c., "of unnatural formation, deviating from the natural order, hideous," a variant of earlier monstruous (late 14c.), from Old French monstruos, monstrueuse and directly from Late Latin monstruosus "strange, unnatural, monstrous," from Latin monstrum "divine omen, portent, sign; abnormal shape; monster, monstrosity," figuratively "repulsive character, object of dread, awful deed, abomination," from root of monere "to admonish, warn, advise," from PIE *moneie- "to make think of, remind," suffixed (causative) form of root *men- (1) "to think."
Meaning "enormous, huge" is from c. 1500; that of "outrageously wrong, shocking, horrible" is from 1570s. The earlier form monstruous remained "very common in the 16th c." [OED]. As an adverb from c. 1600, but by late 19c. regarded as vulgar or colloquial. Related: Monstrously; monstrousness.