Genome editing via CRISPR/Cas9 has rapidly become the tool of choice by virtue of its efficacy and ease of use. However, CRISPR/Cas9-mediated genome editing in clinically relevant human somatic cells remains untested. Here, we report CRISPR/Cas9 targeting of two clinically relevant genes, B2M and CCR5, in primary human CD4+ T cells and CD34+ hematopoietic stem and progenitor cells (HSPCs). Use of single RNA guides led to highly efficient mutagenesis in HSPCs but not in T cells. A dual guide approach improved gene deletion efficacy in both cell types. HSPCs that had undergone genome editing with CRISPR/Cas9 retained multilineage potential. We examined predicted on- and off-target mutations via target capture sequencing in HSPCs and observed low levels of off-target mutagenesis at only one site. These results demonstrate that CRISPR/Cas9 can efficiently ablate genes in HSPCs with minimal off-target mutagenesis, which could have broad applicability for hematopoietic cell-based therapy.