An Etymological Dictionary of the German Language/Annotated/Haube
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Haube, feminine, ‘hood, cap (woman's), crest, tuft,’ from Middle High German hûbe, Old High German hûba, feminine, ‘covering for the head worn by men (Middle High German, especially by soldiers, ‘peaked helmet, steel-cap’) and women’; compare Anglo-Saxon hûfe, in a special sense ‘mitre’; Scandinavian húfa, feminine, ‘cap, hood.’ The cognates are connected by gradation with Haupt (Aryan root kū̆p).