The irradiation of a target with high laser intensity can lead to self-generation of an intense magnetic field (B-field) on the target surface. It has therefore been suggested that the sheath-driven acceleration of high-energy protons would be significantly hampered by the magnetization effect of this self-generated B-field at high enough laser intensities. In this paper, particle-in-cell simulations are used to study this magnetization effect on sheath-driven proton acceleration. It is shown that the inhibitory effect of the B-field on ion acceleration is not as significant as previously thought. Moreover, it is shown that the magnetization effect plays a relatively limited role in high-energy proton acceleration, even at high laser intensities when the mutual coupling and competition between self-generated electric (E-) and B-fields are considered in a realistic sheath acceleration scenario. A theoretical model including the v × B force is presented and confirms that the rate of reduction in proton energy depends on the strength ratio between B- and E-fields rather than on the strength of the B-field alone, and that only a small percentage of the proton energy is affected by the self-generated B-field. Finally, it is shown that the degraded scaling of proton energy at high laser intensities can be explained by the decrease in acceleration time caused by the increased sheath fields at high laser intensities rather than by the magnetic inhibitory effect, because of the longer growth time scale of the latter. This understanding of the magnetization effect may pave the way to the generation of high-energy protons by sheath-driven acceleration at high laser intensities.