Analytical expressions are derived for the spatial coherence function of a speckle field that is generated by the scattering of a Mathieu beam from a random phase mask by following the Fresnel diffraction theory. The general results in the free-space propagation show that the intensity correlation factor is a function of the order of the Mathieu beam, and it evolves spatially as the speckle field propagates. Also, we demonstrate that the intensity correlation factor is non-evolving with the propagation distance in the far-field regime when a lens is placed at the focal distance after the diffuser. The results of this analysis can be used in applications where random fields need to be engineered with structured light beams.