Cataclysmic variables (classical novae and dwarf novae) are binary star systems in which a red dwarf transfers hydrogen-rich matter, by way of an accretion disk, to its white dwarf companion. In dwarf novae, an instability is believed to episodically dump much of the accretion disk onto the white dwarf. The liberation of gravitational potential energy then brightens these systems by up to 100-fold every few weeks or months. Thermonuclear-powered eruptions thousands of times more luminous occur in classical novae, accompanied by significant mass ejection and formation of clearly visible shells from the ejected material. Theory predicts that the white dwarfs in all dwarf novae must eventually accrete enough mass to undergo classical nova eruptions. Here we report a shell, an order of magnitude more extended than those detected around many classical novae, surrounding the prototypical dwarf nova Z Camelopardalis. The derived shell mass matches that of classical novae, and is inconsistent with the mass expected from a dwarf nova wind or a planetary nebula. The shell observationally links the prototypical dwarf nova Z Camelopardalis with an ancient nova eruption and the classical nova process.