'non-' originates from Latin, specifically the word 'non', where it meant 'not'; 'hospital' originates from Latin, specifically the word 'hospitalis', where it meant 'of a guest/host' (related to care); 'acquired' originates from Latin 'acquirere', where 'ad-' meant 'to/toward' and 'quaerere' meant 'to seek or obtain'.

'hospital' changed from Latin 'hospitalis' to Old French 'hospital' and then to Middle English 'hospital', becoming the modern English 'hospital'; 'acquire' came from Latin 'acquirere' to Old French 'acquerre' and Middle English 'acquiren', becoming modern 'acquire' and its past form 'acquired'. The compound 'non-hospital-acquired' is a modern formation combining the negative prefix with established medical terms.

Initially, the components meant 'not' (non-), 'place for guests/care' (hospital), and 'to obtain' (acquire); over time they combined into a modern technical adjective meaning 'not obtained in a hospital setting' (often referring to infections).