At the end of mitosis, eukaryotic cells must segregate both copies of their replicated genome into two new nuclear compartments. They do this either by first dismantling and later reassembling the nuclear envelope in a so-called open mitosis, or by reshaping an intact nucleus and then dividing into two in a closed mitosis. However, while mitosis has been studied in a wide variety of eukaryotes for over a century, it is not known how the double membrane of the nuclear envelope is split into two at the end of a closed mitosis without compromising the impermeability of the nuclear compartment. In studying this problem in the fission yeast Schizosaccharomyces pombe, a classical model for closed mitosis, we use genetics, live cell imaging and electron tomography to show that nuclear fission is achieved via local disassembly of the nuclear envelope (NE) within the narrow bridge that links segregating daughter nuclei. In doing so, we identify a novel inner NE-localised protein Les1 that restricts the process of local NE breakdown (local NEB) to the bridge midzone and prevents the leakage of material from daughter nuclei. The mechanics of local NEB in a closed mitosis closely mirror those of NEB in open mitosis, revealing an unexpectedly deep conservation of nuclear remodelling mechanisms across diverse eukaryotes.