Defects in the architecture or integrity of the nuclear envelope (NE) are associated with a variety of human diseases1. Micronuclei, one common nuclear aberration, are an origin for chromothripsis2, a catastrophic mutational process commonly observed in cancer3–5. Chromothripsis occurs after micronuclei spontaneously lose NE integrity, which generates chromosome fragmentation6. NE disruption exposes DNA to the cytoplasm and initiates innate immune proinflammatory signaling7. Despite its importance, the basis for the NE fragility of micronuclei has not been determined. Here, we demonstrate that micronuclei undergo defective NE assembly: Only “core” NE proteins8,9 assemble efficiently on lagging chromosomes whereas “non-core” NE proteins8,9, including nuclear pore complexes (NPCs), do not. Consequently, micronuclei fail to properly import key proteins necessary for NE and genome integrity. We show that spindle microtubules block NPC/non-core NE assembly on lagging chromosomes, causing an irreversible NE assembly defect. Accordingly, experimental manipulations that position missegregated chromosomes away from the spindle correct defective NE assembly, prevent spontaneous NE disruption, and suppress DNA damage in micronuclei. Thus, during mitotic exit in metazoan cells, chromosome segregation and NE 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.