This paper presents the wave propagation in a tunable phononic crystal consisting of a porous hyperelastic magnetorheological elastomer (MRE) subjected to an external magnetic field. Finite deformations and magnetic induction influence phononic characteristics of the periodic structure through altering the geometry and material properties of the unit cell. The governing equations for incremental time-harmonic plane wave motions superimposed on a static predeformed media are derived. Analytical and finite element (FE) methods are used to investigate dispersion relation and band structure of the phononic crystal for different levels of deformation and applied magnetic induction. It is demonstrated that large deformations and magnetic induction could transform the location and width of band-gaps.