During embryonic development, organs fold into complex shapes that are vital for function. Specific genes are known to regulate organ form, but the mechanical programs by which organ tissues sculpt themselves into shape remain mysterious. Here, we trace the dynamics and mechanical interactions driving inner organ shape change using the embryonic midgut of the fly Drosophila melanogaster. By leveraging deep-tissue light-sheet microscopy for whole-organ live imaging and building a computational framework for extracting tissue deformations in dynamic 3D geometries, we find a mechanical program folding the gut. Hox genes control the emergence of high-frequency calcium pulses, which trigger muscle contractions. These contractions, in turn, induce cell shape change in the adjacent tissue layer, collectively driving a pattern of in-plane tissue deformations. As seen in a simple model, this in-plane pattern is linked to out-of-plane organ folding. These findings offer a mechanical route for gene expression to induce organ shape change: genetic patterning in one layer triggers a physical process to fold the organ into chambers.