  We extend recent work on hydrodynamics with global multipolar symmetries --
known as "fracton hydrodynamics" -- to systems in which the multipolar
symmetries are gauged. We refer to the latter as "fracton
magnetohydrodynamics", in analogy to conventional magnetohydrodynamics (MHD),
which governs systems with gauged charge conservation. We show that fracton MHD
arises naturally from higher-rank Maxwell's equations and in systems with
one-form symmetries obeying certain constraints; while we focus on "minimal"
higher-rank generalizations of MHD that realize diffusion, our methods may also
be used to identify other, more exotic hydrodynamic theories (e.g., with
magnetic subdiffusion). In contrast to semi-microscopic derivations of MHD, our
approach elucidates the origin of the hydrodynamic modes by identifying the
corresponding higher-form symmetries. Being rooted in symmetries, the
hydrodynamic modes may persist even when the semi-microscopic equations no
longer provide an accurate description of the system.
