Defects in the architecture or integrity of the nuclear envelope are associated with a variety of human diseases1. Micronuclei, one common nuclear aberration, are an origin for chromothripsis2, a catastrophic mutational process that is commonly observed in cancer3-5. Chromothripsis occurs after micronuclei spontaneously lose nuclear envelope integrity, which generates chromosome fragmentation6. Disruption of the nuclear envelope exposes DNA to the cytoplasm and initiates innate immune proinflammatory signalling7. Despite its importance, the basis of the fragility of the micronucleus nuclear envelope is not known. Here we show that micronuclei undergo defective nuclear envelope assembly. Only 'core' nuclear envelope proteins8,9 assemble efficiently on lagging chromosomes, whereas 'non-core' nuclear envelope proteins8,9, including nuclear pore complexes (NPCs), do not. Consequently, micronuclei fail to properly import key proteins that are necessary for the integrity of the nuclear envelope and genome. We show that spindle microtubules block assembly of NPCs and other non-core nuclear envelope proteins on lagging chromosomes, causing an irreversible defect in nuclear envelope assembly. Accordingly, experimental manipulations that position missegregated chromosomes away from the spindle correct defective nuclear envelope assembly, prevent spontaneous nuclear envelope disruption, and suppress DNA damage in micronuclei. Thus, during mitotic exit in metazoan cells, chromosome segregation and nuclear envelope assembly are only loosely coordinated by the timing of mitotic spindle disassembly. The absence of precise checkpoint controls may explain why errors during mitotic exit are frequent and often trigger catastrophic genome rearrangements4,5.