'single-leaved' is a compound of 'single' and 'leaved'. 'single' originates from Latin 'singulus' via Old French (e.g. 'sengle' or 'single'), where 'singulus' meant 'one (each)'. 'leaved' is formed from 'leaf' + the adjectival/past participle suffix '-ed', where 'leaf' originates from Old English 'lēaf' meaning 'leaf'.

'singulus' (Latin) became Old French 'sengle'/'single', then Middle English 'single'. 'lēaf' (Old English) became Middle English 'leaf', and the adjective 'leaved' developed by adding '-ed' to indicate possession of leaves; combining them produced the compound adjective 'single-leaved' in modern English.

Initially the components meant 'one' and 'leaf/having leaves'; combined, they originally described 'having a single leaf' and this descriptive botanical meaning has been retained in modern usage as 'having only one leaf'.