'narcotic-induced' is a compound of 'narcotic' and 'induced'. 'narcotic' originates from Greek, specifically the word 'narkotikos', where the root 'nark-' meant 'numbness or stupor'. 'induced' comes from Latin, specifically the word 'inducere', where the prefix 'in-' meant 'into' and 'ducere' meant 'to lead'.

'narcotic' entered English via Medieval Latin/Old French forms derived from Greek 'narkotikos', and 'induce' comes from Latin 'inducere' via Old French/Latin usage; the compound 'narcotic-induced' is a modern English formation combining these elements to describe effects caused by narcotics.

Initially, 'nark-' referred to numbness or stupor and 'induce' to leading into a state; over time the compound came to mean 'caused by narcotics' or 'resulting from narcotic administration'.