In this work, we study the interplay between intrinsic biochemical noise and the diffusive coupling, in an array of three stochastic Brusselators that present a limit-cycle dynamics. The stochastic dynamics is simulated by means of the Gillespie algorithm. The intensity of the intrinsic biochemical noise is regulated by changing the value of the system volume (Ω), while keeping constant the chemical species' concentration. To characterize the system behavior, we measure the average spike amplitude (ASA), the order parameter R, the average interspike interval (ISI), and the coefficient of variation (CV) for the interspike interval. By analyzing how these measures depend on Ω and the coupling strength, we observe that when the coupling parameter is different from zero, increasing the level of intrinsic noise beyond a given threshold suddenly drives the spike amplitude, SA, to zero and makes ISI increase exponentially. These results provide numerical evidence that amplitude death (AD) takes place via a homoclinic bifurcation.