Final organ size and shape result from volume expansion by growth and shape changes by contractility. Complex morphologies can also arise from differences in growth rate between tissues. We address here how differential growth guides the morphogenesis of the growing Drosophila wing imaginal disc. We report that 3D morphology results from elastic deformation due to differential growth anisotropy between the epithelial cell layer and its enveloping extracellular matrix (ECM). While the tissue layer grows in plane, growth of the bottom ECM occurs in 3D and is reduced in magnitude, thereby causing geometric frustration and tissue bending. The elasticity, growth anisotropy and morphogenesis of the organ are fully captured by a mechanical bilayer model. Moreover, differential expression of the Matrix metalloproteinase MMP2 controls growth anisotropy of the ECM envelope. This study shows that the ECM is a controllable mechanical constraint whose intrinsic growth anisotropy directs tissue morphogenesis in a developing organ.