Modeling astrophysical flows in the framework of classical magnetic hydrodynamics often encounters significant difficulties due to high (up to relativistic) Alfven wave velocities. Such situations may arise in modeling the magnetosphere of planets and stars and accretion flows in polars, intermediate polars and near neutron stars. In a strongly magnetized plasma, wave turbulence can develop, which can significantly affect the energy balance and the forces determining the plasma dynamic. In this paper a closed system of equations is obtained for modified magnetic hydrodynamics with wave turbulence for a wide range of magnetic fields and turbulence energies. The turbulent flow is described as the sum of the average flow and perturbations induced by relativistic Alfven waves. Expressions are derived for the volume force, viscosity and turbulence-induced dissipative heating . The analysis of equations for certain limiting cases is performed. It is shown that the proposed approach can be used for modeling a broad class of astrophysical plasma flows.