At zygotic genome activation (ZGA), changes in chromatin structure are associated with new transcription immediately following the maternal-to-zygotic transition (MZT). The nuclear architectural proteins cohesin and CCCTC-binding factor (CTCF) contribute to chromatin structure and gene regulation. We show here that normal cohesin function is important for ZGA in zebrafish. Depletion of the cohesin subunit Rad21 delays ZGA without affecting cell cycle progression. In contrast, CTCF depletion has little effect on ZGA, whereas complete abrogation is lethal. Genome-wide analysis of Rad21 binding reveals a change in distribution from pericentromeric satellite DNA and other locations, including the locus (the products of which are responsible for maternal transcript degradation), to genes, as embryos progress through the MZT. After MZT, a subset of Rad21 binding overlaps the pioneer factor Pou5f3, which activates early expressed genes. Rad21 depletion disrupts the formation of nucleoli and RNA polymerase II foci, suggestive of global defects in chromosome architecture. We propose that Rad21/cohesin redistribution to active areas of the genome is key to the establishment of chromosome organization and the embryonic developmental program.