  In this paper, we derive the post-Newtonian equations of the ideal
Magnetohydrodynamics. To do so, we use the modern approach to post-Newtonian
theory, where the harmonic gauge is used instead of the standard post-Newtonian
gauge, and find the post-Newtonian metric in the presence of the
electromagnetic fields. We show that although the electric field does not
contribute in the metric and curvature of the spacetime, the magnetic field
appears in the time-time component of the metric. The appearance of the
magnetic field, in principle, leads to new relativistic contributions to the
magnetohydrodynamic governing equations. Therefore, using the post-Newtonian
metric, we find the relativistic corrections to the magnetohydrodynamic
equations up to the first post-Newtonian order. In addition, as usage of this
derivation, we obtain a complete set of equations by which the behavior of a
self-gravitating plasma can be determined in post-Newtonian gravity.
