'nonallergenic' is a Modern English formation from the prefix 'non-' (meaning 'not') + 'allergenic'. 'Allergenic' is formed from 'allergy' + the suffix '-genic' ('-genic' from Greek meaning 'producing' or 'causing'). 'Allergy' itself comes from modern New Latin/Greek coinage.

'allergy' was coined in the early 20th century from Greek elements (via New Latin 'allergia'); 'allergic' and related adjectives (e.g. 'allergenic') were derived thereafter, and the negative prefix 'non-' was later attached to form 'nonallergenic'.

Originally the Greek roots in 'allergy' literally referred to an 'altered reaction' (from 'allos' = 'other' and 'ergon' = 'work'), later coming to mean 'hypersensitivity' or 'abnormal immune response'; 'nonallergenic' now means 'not producing such allergic reactions'.