The Weighted Set Covering Problem is a formal model for many practical optimization problems. In this problem the goal is to choose a subset of columns of minimal cost covering every row. Here, we present a novel application of the Artificial Bee Colony algorithm to solve the Weighted Set Covering Problem. The Artificial Bee Colony algorithm is a recent Swarm Metaheuristic technique based on the intelligent foraging behavior of honey bees. Experimental results show that our Artificial Bee Colony algorithm is competitive in terms of solution quality with other recent metaheuristic approaches.