In this work, we address the Manufacturing Cell Formation Problem (MCFP). Cellular Manufacturing is a production strategy that has emerged to reduce materials handling and set up times in order to reduce lead times in production systems and to improve customer’s service levels while reducing costs. We propose a GRASP heuristic to obtain lower bounds for the optimal solution of the problem. To evaluate the performance of the proposed method, we test the heuristic with different instances from the literature and compare the results obtained with those provided by other heuristic methods from the literature. According to the obtained results, the proposed GRASP procedure provides good quality lower bounds with reasonable computational effort.