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 h 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.