At the end of mitosis, eukaryotic cells must segregate the two copies of their replicated genome into two new nuclear compartments1. They do this either by first dismantling and later reassembling the nuclear envelope in an 'open mitosis' or by reshaping an intact nucleus and then dividing it into two in a 'closed mitosis'2,3. Mitosis has been studied in a wide variety of eukaryotes for more than a century4, but 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 remains unknown5. Here, using the fission yeast Schizosaccharomyces pombe (a classical model for closed mitosis5), genetics, live-cell imaging and electron tomography, we show that nuclear fission is achieved via local disassembly of nuclear pores within the narrow bridge that links segregating daughter nuclei. In doing so, we identify the protein Les1, which is localized to the inner nuclear envelope and restricts the process of local nuclear envelope breakdown to the bridge midzone to prevent the leakage of material from daughter nuclei. The mechanism of local nuclear envelope breakdown in a closed mitosis therefore closely mirrors nuclear envelope breakdown in open mitosis3, revealing an unexpectedly high conservation of nuclear remodelling mechanisms across diverse eukaryotes.