Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR) technology has revolutionized genetic medicine by enabling precise genome editing for therapeutic benefit. CRISPR nucleases are programmed to target genomic sites with sequence complementarity to the spacer region of an associated guide RNA. However, these nucleases may target genomic loci with sequences similar to the target site, which can lead to unintended disruption of off-target genes. The risks associated with these off-target editing events are critical to assess as CRISPR-based in vivo editing systems advance to clinical development. Nonhuman primates (NHPs) are common model species for evaluating the human safety of many therapeutic modalities, but their relevance for evaluating human CRISPR off-target activity has yet to be determined. In this study, 1,220,908 Cas12a and 6,159,066 Cas9 spacer sequences targeting human genes were designed, and off-target editing sites were computationally predicted in humans and five common NHP species. Of the 7,413 Cas12a and 570,754 Cas9 spacers meeting defined on- and off-target inclusion criteria, only 14-21% of Cas12a and 7-15% of Cas9 human off-targets per spacer are recapitulated in the genomes of NHPs commonly used in preclinical studies. These results highlight the limitations of NHPs for the study of human CRISPR spacer specificity and contextualize human risk informed by these studies.