We calculate the Thomson scattering cross section in a non-relativistic, magnetized, high density plasma -- in a regime where collective excitations can be described by magnetohydrodynamics. We show that, in addition to cyclotron resonances and an elastic peak, the cross section exhibits two pairs of peaks associated with slow and fast magnetosonic waves; by contrast, the cross section arising in pure hydrodynamics possesses just a single pair of Brillouin peaks. Both the position and the width of these magnetosonic-wave peaks depend on the ambient magnetic field and temperature, as well as transport and thermodynamic coefficients, and so can therefore serve as a diagnostic tool for plasma properties that are otherwise challenging to measure.
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