The possibility of control and tuning of the band structures of phononic crystals offered by the introduction of an active magnetoelastic material and the application of an external magnetic field is studied. Two means to obtain large elastic properties variations in magnetoelastic material are considered: Giant magnetostriction and spin reorientation transition effects. A plane wave expansion method is used to calculate the band structures. The magnetoelastic coupling is taken into account through the consideration of an equivalent piezomagnetic material model with elastic, piezomagnetic, and magnetic permeability tensors varying as a function of the amplitude and orientation of the applied magnetic field. Results of contactless tunability of the absolute bandgap are presented for a two-dimensional phononic crystal constituted of Terfenol-D square rod embedded in an epoxy matrix