  We have performed the leading order perturbative calculation to obtain the
equation of state (EoS) of the strange quark matter (SQM) at zero temperature
under the magnetic field B = 10^18 G. The SQM comprises two massless quark
flavors (up and down) and one massive quark flavor(strange). Consequently, we
have used the obtained EoS to calculate the maximum gravitational mass and the
corresponding radius of the magnetized strange quark star (SQS). We have
employed two approaches, including the regular perturbation theory (RPT) and
the background perturbation theory (BPT). In RPT the infrared (IR) freezing
effect of the coupling constant has not been accounted for, while this effect
has been included in BPT. We have obtained the value of the maximum
gravitational mass to be more than three times the solar mass. The validity of
isotropic structure calculations for SQS has also been investigated. Our
results show that the threshold magnetic field from which an anisotropic
approach begins to be significant lies in the interval 2*10^18G < B < 3*10^18G.
Furthermore, we have computed the redshift, compactness and Buchdahl-Bondi
bound of the SQS to show that this compact object cannot be a black hole.
