•We report the magnetic field-enabled propagation of solitary waves.•We propose to exploit the unique magneto-mechanical coupling of hard-magnetic active elastomers to remotely tune the width, amplitude, and velocity of the nonlinear solitary waves propagating within.•This work provide a fundamental understanding of the effects of magneto-mechanical coupling on the unusual nonlinear vector solitary wave phenomenon. We propose a design of a metamaterial for magnetically tunable propagation of nonlinear vector solitary waves. The metamaterial consists of a periodic array of units of hard-magnetic inclusion embedded in a soft matrix. The units are connected via thin and highly deformable ligaments. Our theoretical and numerical modeling results show that the configuration of the metamaterial undergoes drastic transformations when activated by a magnetic field. These controllable microstructural transformations significantly influence the propagation of vector solitary waves in the proposed metamaterial system. We report the magnetic field-enabled propagation of solitary waves. We show that the proposed soft magnetoactive metamaterial allows us to tune the key characteristics of the enabled nonlinear solitary waves, including their pulse width and amplitude. Our findings also highlight the potential of magneto-mechanical coupling in the development of untethered mechanical metamaterial systems for applications in nondestructive testing, energy harvesting, and smart soft wave devices.