'non-asbestos' is formed from the English prefix 'non-' (meaning 'not') plus 'asbestos'. 'non-' comes from Old and Middle English (related to Latin 'non') where it served as a negating prefix; 'asbestos' originates from Greek 'asbestós', meaning 'inextinguishable' or 'unquenchable'.

'asbestós' (Greek) entered English via Latin/Medieval Latin as 'asbestos' to denote fire-resistant mineral fibers; in Modern English the negating prefix 'non-' was attached to produce 'non-asbestos' to describe materials that do not contain asbestos.

Initially 'asbestós' meant 'inextinguishable' (referring to fire-resistant quality); over time it came to name specific fibrous minerals used for their fire resistance, and 'non-asbestos' evolved to mean 'not containing those asbestos minerals.'