In this paper, we are concerned with the Cauchy problem of the multi-dimensional inhomogeneous incompressible magnetohydrodynamic equations with fractional dissipation. We prove the unique global strong solution with vacuum to the magnetohydrodynamic equations over the whole space. In addition, the large time decay rates of the corresponding strong solution are also obtained. Note that our result is proved without any smallness on the initial data. Moreover, the initial density is allowed to be nonnegative, and in particular, the initial vacuum is allowed. To our best knowledge, this is the first result on the inhomogeneous fractional magnetohydrodynamic equations.