Magnetoelectric materials convert magnetic fields to electric fields and have applications in wireless data and power transmission, electronics, sensing, data storage, and biomedical technology. For example, magnetoelectrics could enable precisely timed remote stimulation of neural tissue, but the resonance frequencies where magnetoelectric effects are maximized are typically too high to stimulate neural activity. To overcome this challenge, we created the first self-rectifying magnetoelectric "metamaterial." This metamaterial relies on nonlinear charge transport across semiconductor layers that allow the material to generate a steady bias voltage in the presence of an alternating magnetic field. This "self-rectification" allows us to generate arbitrary electrical pulse sequences that have a time-averaged voltage in excess of 1 V. As a result, we can use magnetoelectric nonlinear metamaterials (MNMs) to remotely stimulate peripheral nerves with repeatable latencies of less than 5 ms, which is more than 120 times faster than previous neural stimulation approaches based on magnetic materials. These short latencies enable this metamaterial to be used in applications where fast neural signal transduction is necessary such as in sensory or motor neuroprosthetics. As a proof or principle, we show wireless stimulation to restore a sensory reflex in an anesthetized rat model as well as using the MNM to restore signal propagation in a severed nerve. The rational design of nonlinearities in the magnetic-to-electric transduction pathway as described here opens the door to many potential designs of MNMs tailored to applications spanning electronics, biotechnology, and sensing.