We have analyzed the self-action effects in the propagation of surface magnetostatic wave (SMSW) pulses in a 1D magnonic crystal–dielectric–metal structure in which the region of anomalous dispersion controlled by the selection of thickness of the insulator and ensuring the fulfillment of the Lighthill criterion in the generation of SMSW solitons is formed. It is shown that when the metallization-induced region of anomalous dispersion coincides with the Bragg resonance frequency range, no SMSW solitons form.