'nonarthritic' is formed from the negative prefix 'non-' and the adjective 'arthritic'. 'non-' originates from Latin, specifically the word 'non', where 'non' meant 'not'. 'arthritic' originates ultimately from Greek 'arthron' meaning 'joint' combined with the suffix derived from Greek 'itis' (inflammation).

'arthritic' derives from Greek 'arthron' ('joint') → Late Latin/Medieval Latin 'arthriticus' → Middle English forms and eventually the modern English adjective 'arthritic'. The prefix 'non-' (from Latin 'non') was attached in Modern English to form 'nonarthritic' meaning 'not arthritic'.

Originally related to 'inflammation of the joints' (as in 'arthritic' = 'pertaining to joint inflammation'), the composite 'nonarthritic' has consistently meant 'not affected by arthritis' and has retained that negative/absence-of-disease sense.