'one-syllable' originates from Modern English, formed by compounding 'one' and 'syllable' (the former from Old English 'ān', the latter from Latin/Greek via Old French).

'syllable' changed from Greek 'syllabē' to Latin 'syllaba', passed into Old French and Middle English as forms like 'sillable'/'syllable', and eventually became the modern English 'syllable'; 'one' comes from Old English 'ān' (from Proto-Germanic *ainaz). The compound 'one-syllable' developed in Modern English by combining these elements to describe words with a single syllable.

Originally (Greek) 'syllabē' meant 'that which is sounded together'; over time it came to mean a unit of pronunciation or 'syllable', and the compound 'one-syllable' now means 'having or being a single syllable'.