Strange quark matter could be found in the core of neutron stars or forming strange quark stars. As is well known, these astrophysical objects are endowed with strong magnetic fields that affect the microscopic properties of matter and modify the macroscopic properties of the system. In this article we study the role of a strong magnetic field in the thermodynamical properties of a magnetized degenerate strange quark gas, taking into account β-equilibrium and charge neutrality. Quarks and electrons interact with the magnetic field via their electric charges and anomalous magnetic moments. In contrast to the magnetic field value of 10¹⁹ G, obtained when anomalous magnetic moments are not taken into account, we find the upper bound B<8.6×10¹⁷ G, for the stability of the system. A phase transition could be hidden for fields greater than this value.