Within the maximum entropy principle, we present a general theory able to describe in a dynamical context the transport properties of hot carriers in monolayer graphene under electric fields of arbitrary strength. Therefore, we obtain a closed extended hyperbolic system of hydrodynamic (HD) equations in which all the unknown constitutive functions are completely determined. In particular, we consider the different scattering mechanisms used in the literature in the kinetic approaches. The closed extended HD system is applied to monolayer graphene at 300 K and is validated by comparing numerical calculations with ensemble Monte Carlo simulations.