Parametric feature grid encodings have gained significant attention as an encoding approach for intrinsic neural fields since they allow for much smaller MLPs which decreases the inference time of the models significantly. In this work, we propose MeshFeat, a parametric feature encoding tailored to meshes, for which we adapt the idea of multi-resolution feature grids from Euclidean space. We start from the structure provided by the given vertex topology and use a mesh simplification algorithm to construct a multi-resolution feature representation directly on the mesh. The approach allows the usage of small MLPs for neural fields on meshes, and we show a significant speed-up compared to previous representations while maintaining comparable reconstruction quality for texture reconstruction and BRDF representation. Given its intrinsic coupling to the vertices, the method is particularly well-suited for representations on deforming meshes, making it a good fit for object animation.