'vase-like' is a Modern English compound formed from 'vase' + the suffix '-like' (meaning 'having the form of' or 'similar to'). 'Vase' entered English from French 'vase', ultimately from Latin 'vas' meaning 'vessel'.

'vase' comes from Latin 'vas' ('vessel'), passed into Old French/Modern French as 'vase' and was borrowed into English; '-like' derives from Old English 'līc' meaning 'body, form' and developed into the productive suffix '-like' in Modern English to form adjectives such as 'vase-like'.

Initially, 'vase' simply meant 'a vessel' (Latin 'vas'); over time English use narrowed to the decorative container sense 'vase', and the compound 'vase-like' now specifically means 'having the shape or appearance of a vase'.