Different energy-dissipating devices have been proposed in the literature to attenuate the destructive effects of base excitations over fluid storage tanks. These structures have numerous applications in strategic industries and their failure can result in environmental hazards and huge economic losses. Proposed techniques in the literature for seismic energy dissipation of fluid-contained tanks are mostly centred on passive and active control mechanisms. Semi-active control devices using materials with adjustable properties offer advantages of both active and passive systems while removing their drawbacks. In this paper, the performance of a Magnetorheological (MR) damper on the seismic response reduction of fluid storage tanks through the application of three different control strategies including H2/LQG, PID, FOPID, and two passive techniques, i.e. Passive On, and Passive Off has been investigated. Parameters of the semi-active controllers are optimally designed for each aspect ratio and the applied ground motion using the Hunger Game Search (HGS) technique and finally, the semi-active Clipping algorithm commands the voltage to the damper. The fluid-tank-MR damper system has been examined under three Far-Fault and three Near-Fault ground motions. Numerical simulations have demonstrated that depending on the aspect ratio, applied ground motion, and the control strategy, the MR damper can mitigate the peak relative displacements and absolute accelerations of the two major modes of the system, i.e the rigid and impulsive modes, up to 72% and 67%, respectively. This proves the efficacy of these dampers in reducing the maximum base shear and overturning moment, hence mitigating the damage risks in these structures.