The design of ordered arrays of metal nanoclusters such as, for example, two-dimensional cluster-organic frameworks might open a new route toward the development of materials with tailored optical properties. Such systems could serve as plasmonically enhanced light-harvesting materials, sensors, or catalysts. We present here a theoretical approach for the simulation of the optical properties of ordered arrays of metal clusters that is based on the ab initio parametrized Frenkel exciton model. We demonstrate that small atomically precise silver clusters can be assembled in one- and two-dimensional arrays on suitably designed porphyrin templates exhibiting remarkable optical properties. By employing explicit time-dependent density functional theory calculations on smaller homologues, we show that the intrinsic optical properties of metal clusters are largely preserved but undergo J- and H-type excitonic coupling that results in controllable splitting of their excited states. Furthermore, ab initio parametrized Frenkel exciton model calculations allow us to predict an energetic splitting of up to 0.77 eV in extended two-dimensional square arrays and 0.79 eV in tilted square aggregates containing up to 25 cluster-porphyrin subunits.