In this work, a novel hybrid-order subcell method for the Discontinuous Galerkin method is presented. The subcell method is devised to locally stabilize the Discontinuous Galerkin method with the intention of enabling multiscale hyperbolic flow simulations for which the increased accuracy of the Discontinuous Galerkin method is needed but for which it is nominally unstable. The method allows for independent limiting of each degree of freedom, at variable order such as to continuously balance robustness and accuracy using specific limiting criterions. The computational footprint of the hybrid-order subcell method is slightly higher than that of vanilla Discontinuous Galerkin, and is therefore only used where needed. The subcell method relies on a low order subcell basis constructed from the Voronoi tessellation of each mesh element. The Voronoi tessellation uses the polynomial nodes of the Discontinuous Galerkin scheme as its cell centers. That way the two bases are guaranteed to be of the same size, making projection between the subcell space and the high-order polynomial space trivial. The low order subcell basis is convolved with the high-order polynomial basis to form a second, high-order, subcell basis. The blending between these two subcell bases, is what yields the hybrid order nature of the method. The method is implemented in the Discontinuous Galerkin solver Argo, where its performance is evaluated and compared against existing approaches. In particular, the proposed scheme is benchmarked against the subcell flux-limiting strategy of Vilar et al. [1]. Numerical experiments are conducted using the two-dimensional Navier–Stokes equations for an ideal gas as a stepping stone towards the more intricate physics of three-dimensional hypersonic flows.