  Magnetized strange quark stars, composed of strange quark matter (SQM) and
self-bound by strong interactions, can be formed if the energy per baryon of
magnetized SQM is less than that of the most stable $^{56}$Fe nucleus under the
zero external pressure and temperature. Utilizing the MIT bag model description
of magnetized SQM under charge neutrality and beta equilibrium conditions, the
corresponding absolute stability window in the parameter space of the theory is
determined. It is shown that there exists the maximum magnetic field strength
allowed by the condition of absolute stability of magnetized SQM. The value of
this field, $H\sim3\cdot10^{18}$ G, represents the upper bound on the magnetic
field strength which can be reached in a strongly magnetized strange quark
star.
