'sparsely-veined' originates from Modern English, combining 'sparsely' (from 'sparse' + suffix '-ly') and 'veined' (the past-participial/adjectival form of 'vein'). 'sparse' ultimately comes from Latin 'sparsus' via Latin/French, where 'sparsus' (from 'spargere') meant 'scattered'; 'vein' comes from Old French 'veine', from Latin 'vena' meaning 'vein'.

'sparse' developed from Latin 'sparsus' (> Old French/Medieval Latin forms) into Early Modern English 'sparse'; 'vein' passed from Latin 'vena' to Old French 'veine' and then into Middle English as 'vein'; the adjectival form 'veined' is formed from the past participle of the verb 'to vein' or as a participial adjective meaning 'having veins', and the compound 'sparsely-veined' arose in Modern English by combining the adverbial modifier with that participial adjective.

Initially, elements meant 'scattered' ('sparse') and 'a vessel or ridge' ('vena/vein'); over time the compound came to mean specifically 'having veins that are scattered or few', used especially in botanical and anatomical descriptions.