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 =1018G. 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). InRPTthe infrared (IR) freezing effect of the coupling constant has not been accounted for, while this effect has been included inBPT. 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 ×1018G
