Phononic crystals are periodic structures consist of different materials in an elastic medium designed to interact with elastic waves. These crystals have practical applications, such as, frequency filters, beam splitters, sound or vibration protectors, acoustic lasers, acoustic mirrors and elastic waveguides. In this study, the wave propagation in a tunable phononic crystal is investigated. The magnetically controllable phononic crystal consists of a soft magnetorheological elastic medium undergoing large deformations upon the application of a magnetic field. Finite deformations and induced magnetic fields influence wave propagation characteristics in the periodic structure. The soft matrix is modeled as a hyperelastic elastomer to take into account the material nonlinearity. The integrated effects of material properties, transformation of the geometry of the unit cell, and the induced magnetic field, are used to tune the band structure of the periodic structure. Both analytical and finite element methods are employed to evaluate the dispersion diagrams considering Bloch boundary conditions. Results show that the applied magnetic field significantly affect the width and the position of band-gaps.