An Etymological Dictionary of the German Language/Annotated/Sprosse
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Sprosse, feminine, ‘shoot, sprout; rung,’ from Middle High German sproȥȥe, Old High German sproȥȥo, masculine, ‘rung.’ This meaning is probably derived from an older signification (‘twig’); compare Old Icelandic sprote, ‘twig, rod, staff,’ Anglo-Saxon sprota, ‘twig.’ These terms are connected with the Teutonic root sprū̆t in sprietzen, of which Sproß, ‘sprout,’ is a Modern High German derivative; from the latter Sprößling is derived.