In this paper we generalize earlier gasdynamic analyses of the motion of the heliospheric termination shock in response to upstream disturbances (Barnes, 1993, 1994; Naidu and Barnes, 1994), to include magnetohydrodynamic (MHD) phenomena. We assume that the termination shock is a strong, perpendicular shock and that the initial upstream disturbance is a tangential discontinuity. The resulting configuration after the interaction is very similar to that in the gasdynamic models after an interation with a contact discontinuity or interplanetary shock, and for an increase (decrease) in dynamic pressure consists of an outward (inward) propagating termination shock and an outward propagating shock (MHD rarefaction wave) that carries the signal of the disturbance into the far downstream plasma. The plasma immediately behind the new termination shock is separated from the downstream signal by a tangential discontinuity. The results of the model show that the speed of the new termination shock depends mainly on the magnitude of the change in dynamic pressure and are typically of order ~100 km/s, comparable to the results of the gasdynamic models.