'fever-reducing' is a compound of 'fever' + 'reducing'. 'fever' originates from Old English 'fēfor', ultimately from Latin 'febris'. 'reduce' (present participle 'reducing') originates from Latin 'reducere', where 're-' meant 'back' and 'ducere' meant 'to lead'.

'fever' passed from Latin 'febris' into Old English as 'fēfor' and then into Middle English as 'fever'. 'reduce' came from Latin 'reducere' through Old French 'reduire' into Middle English 'reduce', with the participle form later forming 'reducing'. The modern compound 'fever-reducing' is a straightforward combination of these elements in modern English.

Initially, 'fever' referred to a state of heat or fever (from Latin), and this basic meaning has been retained. 'Reduce' initially meant 'to lead back' in Latin; over time it came to mean 'make smaller or less', which is the sense used in 'fever-reducing' (to lessen fever).