'fever-suppressing' is a modern compound formed from 'fever' + the present participle of 'suppress'; 'fever' originates from Old English 'fēfor' (from a Germanic reflex influenced by Latin 'febris'), and 'suppress' originates from Latin 'supprimere' ('sub-' meaning 'under' + 'premere' meaning 'to press').

'suppress' entered English via Old French and Middle English from Latin 'supprimere'/'suppressus', while 'fever' has been present in Old English ('fēfor') with continued use into modern English; the compound 'fever-suppressing' is a transparent modern English formation combining the two elements.

Initially, 'suppress' had the literal sense 'to press down' (from Latin), and over time it developed the figurative senses 'to put an end to' or 'to check'; combined with 'fever', the modern sense became 'to reduce or check fever'.