Cohesin is important for 3D genome organization. Nevertheless, even the complete removal of cohesin has surprisingly little impact on steady-state gene transcription and enhancer activity. Here we show that cohesin is required for the core transcriptional response of primary macrophages to microbial signals, and for inducible enhancer activity that underpins inflammatory gene expression. Consistent with a role for inflammatory signals in promoting myeloid differentiation of hematopoietic stem and progenitor cells (HPSCs), cohesin mutations in HSPCs led to reduced inflammatory gene expression and increased resistance to differentiation-inducing inflammatory stimuli. These findings uncover an unexpected dependence of inducible gene expression on cohesin, link cohesin with myeloid differentiation, and may help explain the prevalence of cohesin mutations in human acute myeloid leukemia.