'self-moved' originates from the English prefix 'self' (Old English 'self') combined with the past participle 'moved' of the verb 'move' (from Latin 'movere').

'move' changed from Latin 'movere' to Old French forms (e.g. 'movoir') and into Middle English as 'moven'/'move', eventually becoming modern English 'move'; 'self' comes from Old English 'self' and the compound 'self-' + past participle patterns have long been used in English to form adjectives (e.g. 'self-taught').

Initially the components referred literally to 'self' + 'moved' (i.e., moved by itself); over time the compound has been used both literally (self-propelled) and figuratively (acting on one's own initiative).