Magnon blockade is an effective physical mechanism to generate a single magnon, which is of great importance in quantum information processing. We present a scheme to realize the unconventional magnon blockade effect by using Kerr nonlinearity in a cavity electromagnonic system. Under weak driving conditions, we give the optimal parameter conditions for magnon antibunching through analytical calculations, which are in good agreement with numerical results. Furthermore, we find that Kerr nonlinearity is necessary to create magnon blockade. In particular, unconventional magnon blockade can be achieved in both weak nonlinearity and weak coupling regimes. The present scheme indicates a method for generating unconventional magnon blockade effect and provides a feasible and flexible platform for the realization of a single-magnon source with high purity.