'vermin-infested' is a compound of the noun 'vermin' and the past-participle adjective 'infested'. 'vermin' originates from Old French 'vermin', ultimately from Latin 'vermis' meaning 'worm'; 'infest' comes from Latin 'infestare' meaning 'to attack or disturb'.

'vermin' entered Middle English from Old French 'vermin' (from Latin 'vermis'); 'infest' came into English from Latin 'infestare' via Old French/Anglo-Norman and developed the past-participle form 'infested'; the productive pattern 'X-infested' (e.g. 'rat-infested', 'vermin-infested') arose in modern English to describe places overrun by pests.

Initially 'vermin' referred specifically to worms and parasitic creatures, but it broadened to mean small harmful animals (rats, insects). 'Infest' originally meant 'to attack or harass' and has narrowed in common use to describe being present in large numbers as pests; together the compound now means 'overrun by pests'.