'anti-narcotic' originates from Greek and New Latin elements: the prefix 'anti-' (from Greek 'anti' meaning 'against') combined with 'narcotic' (from Greek 'narkōtikós' via Latin/French, related to 'narkē' meaning 'numbness').

'narkōtikós' in Greek passed into Late Latin and Old French as words meaning substances that cause numbness; the English 'narcotic' was formed from these and later combined with the prefix 'anti-' to produce 'anti-narcotic' and its plural 'anti-narcotics'.

Initially, related words meant 'causing numbness' (referring to numbing substances); over time 'narcotic' narrowed to mean 'drugs, especially illegal or controlled drugs,' and 'anti-narcotic(s)' came to mean 'against such drugs' or 'aimed at combating them.'