Children show a higher incidence of leukemia compared to young adolescents, yet their cells have less age-related (oncogenic) somatic mutations. Newborns with Down syndrome have an even higher risk of developing leukemia, which is thought to be driven by mutations that accumulate during fetal development. To characterize mutation accumulation in individual stem and progenitor cells of Down syndrome and karyotypically normal fetuses, we clonally expanded single cells and performed whole-genome sequencing. We found a higher mutation rate in haematopoietic stem and progenitor cells during fetal development compared to the post-infant rate. In fetal trisomy 21 cells the number of somatic mutations is even further increased, which was already apparent during the first cell divisions of embryogenesis before gastrulation. The number and types of mutations in fetal trisomy 21 haematopoietic stem and progenitor cells were similar to those in Down syndrome-associated myeloid preleukemia and could be attributed to mutational processes that were active during normal fetal haematopoiesis. Finally, we found that the contribution of early embryonic cells to human fetal tissues can vary considerably between individuals. The increased mutation rates found in this study, may contribute to the increased risk of leukemia early during life and the higher incidence of leukemia in Down syndrome.