'inflammation-reducing' is a modern compound formed from 'inflammation' (a noun) and the present participle 'reducing'. 'Inflammation' originates from Latin 'inflammatio', where 'in-' meant 'in' or 'on' and 'flammare' meant 'to set on fire'. 'Reduce' originates from Latin 'reducere', where 're-' meant 'back' and 'ducere' meant 'to lead'.

The element 'inflammation' passed into Middle English via Old French and Late Latin as 'inflammatio', and 'reduce' came into English from Old French and Latin 'reducere'; the compound adjective form ('inflammation-reducing') is a productive modern English formation combining an established medical noun with a present-participle verb form.

Initially, 'inflammation' referred to the act of setting on fire or a metaphorical 'burning' (literal and medical), and 'reduce' meant 'lead back' or 'bring down'; over time the combined sense evolved into the practical modern meaning 'capable of lessening or suppressing inflammation'.