The cohesin complex spatially organizes interphase chromatin by bringing distal genomic loci into close physical proximity, looping out the intervening DNA. Mutation of cohesin complex subunits is observed in cancer and developmental disorders, but the mechanisms through which these mutations may contribute to disease remain poorly understood. Here, we investigate a recurrent missense mutation to the hinge domain of the cohesin subunit SMC1A, observed in acute myeloid leukemia. Engineering this mutation into murine embryonic stem cells caused widespread changes in gene expression, including dysregulation of the pluripotency gene expression program. This mutation reduced cohesin levels at promoters and enhancers, decreased DNA loops and interactions across short genomic distances, and weakened insulation at CTCF-mediated DNA loops. These findings provide insight into how altered cohesin function contributes to disease and identify a requirement for the cohesin hinge domain in three-dimensional chromatin structure.