CRISPR-Cas9 genome editing has potential to cure diseases without current treatments, but therapies must be safe. Here we show that CRISPR-Cas9 editing can introduce unintended mutations in vivo, which are passed on to the next generation. By editing fertilized zebrafish eggs using four guide RNAs selected for off-target activity in vitro, followed by long-read sequencing of DNA from >1100 larvae, juvenile and adult fish across two generations, we find that structural variants (SVs), i.e., insertions and deletions ≥50 bp, represent 6% of editing outcomes in founder larvae. These SVs occur both at on-target and off-target sites. Our results also illustrate that adult founder zebrafish are mosaic in their germ cells, and that 26% of their offspring carries an off-target mutation and 9% an SV. Hence, pre-testing for off-target activity and SVs using patient material is advisable in clinical applications, to reduce the risk of unanticipated effects with potentially large implications.