The travel of a tsunami wave is accompanied by generation of geomagnetic field perturbation and acoustic-gravity wave (AGW) propagating into the ionosphere. We consider a mechanism of electric current generation by the tsunami wave in the ocean and ionosphere. The electric current in the ocean is generated by motion of conducting seawater in geomagnetic field, and in the conducting ionosphere it is generated by AGW propagation from the atmosphere. The electric current in the ionosphere may be greater than in the seawater due to exponential increase of amplitude of the upward-propagating AGW. The equations of magnetic field in the “ocean-atmosphere-ionosphere” model in the inclined magnetic field were derived. The spatial distribution of the magnetic field perturbation in the atmosphere and ionosphere was calculated. It is shown that the electric current in the ionosphere significantly changes the geomagnetic field perturbation. An influence of the geomagnetic field inclination on its perturbation is analyzed. Our results demonstrate a possibility of satellite monitoring of tsunami wave based on recording electromagnetic field in the middle and low latitudes.