Using full opto-acoustic numerical simulations, we demonstrate enhancement and suppression of the SBS gain in a metamaterial comprising a subwavelength cubic array of dielectric spheres suspended in a dielectric background material. We develop a general theoretical framework and present several numerical examples using technologically important materials. For $As_2S_3$ spheres in silicon, we achieve a gain enhancement of more than an order of magnitude compared to pure silicon and for GaAs spheres in silicon, full suppression is obtained. The gain for $As_2S_3$ glass can also be strongly suppressed by embedding silica spheres. The constituent terms of the gain coefficient are shown to depend in a complex way on the filling fraction. We find that electrostriction is the dominant effect behind the control of SBS in bulk media.