Aneuploidy that arises during meiosis and/or mitosis is a major contributor to early embryo loss. We previously showed that human preimplantation embryos encapsulate missegregated chromosomes into micronuclei while undergoing cellular fragmentation and that fragments can contain chromosomal material, but the source of this DNA was unknown. Here, we leveraged the use of a nonhuman primate model and single-cell DNA-sequencing (scDNA-seq) to examine the chromosomal content of 471 individual samples comprising 254 blastomeres, 42 polar bodies, and 175 cellular fragments from a large number (N = 50) of disassembled rhesus cleavage-stage embryos. Our analysis revealed that the aneuploidy and micronucleation frequency is conserved between humans and macaques, and that fragments encapsulate whole and/or partial chromosomes lost from blastomeres. Single-cell/fragment genotyping showed that these chromosome-containing cellular fragments (CCFs) can be maternally or paternally derived and display double-stranded DNA breaks. DNA breakage was further indicated by reciprocal subchromosomal losses/gains between blastomeres and large segmental errors primarily detected at the terminal ends of chromosomes. By combining time-lapse imaging with scDNA-seq, we determined that multipolar divisions at the zygote or two-cell stage were associated with CCFs and generated a random mixture of chromosomally normal and abnormal blastomeres with uniparental or biparental origins. Despite frequent chromosome missegregation at the cleavage-stage, we show that CCFs and nondividing aneuploid blastomeres showing extensive DNA damage are prevented from incorporation into blastocysts. These findings suggest that embryos respond to chromosomal errors by encapsulation into micronuclei, elimination via cellular fragmentation, and selection against highly aneuploid blastomeres to overcome chromosome instability during preimplantation development.