Micronuclei (MN) are a commonly used marker of chromosome instability that form when missegregated chromatin recruits its own nuclear envelope (NE) after mitosis. MN frequently rupture, which results in genome instability, upregulation of metastatic genes, and increased immune signaling. MN rupture is linked to NE defects, but the cause of these defects is poorly understood. Previous work from our lab found that chromosome identity correlates with rupture timing for small MN, i.e. MN containing a short chromosome, with more euchromatic chromosomes forming more stable MN with fewer nuclear lamina gaps. Here we demonstrate that histone methylation promotes rupture and nuclear lamina defects in small MN. This correlates with increased MN size, and we go on to find that all MN have a constitutive nuclear export defect that drives MN growth and nuclear lamina gap expansion, making the MN susceptible to rupture. We demonstrate that these export defects arise from decreased RCC1 levels in MN and that additional loss of RCC1 caused by low histone methylation in small euchromatic MN results in additional import defects that suppress nuclear lamina gaps and MN rupture. Through analysis of mutational signatures associated with early and late rupturing chromosomes in the Pan-Cancer Analysis of Whole Genomes (PCAWG) dataset, we identify an enrichment of APOBEC and DNA polymerase E hypermutation signatures in chromothripsis events on early and mid rupturing chromosomes, respectively, suggesting that MN rupture timing could determine the landscape of structural variation in chromothripsis. Our study defines a new model of MN rupture where increased MN growth, caused by defects in protein export, drives gaps in nuclear lamina organization that make the MN susceptible to membrane rupture with long-lasting effects on genome architecture.