Genome editing has therapeutic potential for treating genetic diseases and cancer. However, the currently most practicable approaches rely on the generation of DNA double-strand breaks (DSBs), which can give rise to a poorly characterized spectrum of chromosome structural abnormalities. Here, using model cells and single-cell whole-genome sequencing, as well as by editing at a clinically relevant locus in clinically relevant cells, we show that CRISPR–Cas9 editing generates structural defects of the nucleus, micronuclei and chromosome bridges, which initiate a mutational process called chromothripsis. Chromothripsis is extensive chromosome rearrangement restricted to one or a few chromosomes that can cause human congenital disease and cancer. These results demonstrate that chromothripsis is a previously unappreciated on-target consequence of CRISPR–Cas9-generated DSBs. As genome editing is implemented in the clinic, the potential for extensive chromosomal rearrangements should be considered and monitored. Chromothripsis, a chromosomal shattering event, can be elicited by micronuclei and chromosome bridges formed by CRISPR–Cas9-generated double-stranded breaks. Extensive chromosomal rearrangements may thus be an on-target effect of genome editing.