Sedimentary rocks often exhibit a transverse isotropy due to fine scale layering. We investigate the effect of the anisotropy of fracture toughness on the propagation of a planar 3D hydraulic fracture perpendicular to the isotropy plane: a configuration commonly encountered in sedimentary basins. We extend a fully implicit level set scheme for the simulation of hydraulic fracture growth to the case of anisotropic fracture toughness. We derive an analytical solution for the propagation of an elliptical hydraulic fracture in the toughness dominated regime—a shape which results from a particular form of toughness anisotropy. The developed numerical solver closely matches this solution as well as classical benchmarks for hydraulic fracture growth with isotropic toughness. We then quantify numerically the transition between the viscosity dominated propagation regime at early time—where the fracture grows radially—to the toughness dominated regime at large time where the fracture reaches an elliptical shape in the case of an elliptical anisotropy. The time scale at which the fracture starts to deviate from the radial shape and gets more elongated in the direction of lower toughness is in accordance with the viscosity to toughness transition time-scale for a radial fracture defined with the largest value of fracture toughness. Similarly, the toughness dominated regime is fully reached along the whole fracture front when the time gets significantly larger than the same transition time-scale defined with the lowest value of toughness. Using different toughness anisotropy functions, we also illustrate how the details of the complete variation of fracture toughness with propagation direction governs the final hydraulic fracture shape at large time. Our results highlight toughness anisotropy as a possible hydraulic fracture height containment mechanism as well as the need for its careful characterization beyond measurements in the sole material axes (divider and arrester) directions.