Categorical data clustering has been gaining significant attention from researchers since the last few years, because most of the real life data sets are categorical in nature. In contrast to numerical domain, no natural ordering can be found among the elements of a categorical domain. Hence no inherent distance measure, like the Euclidean distance, would work to compute the distance between two categorical objects. Most of the clustering algorithms designed for categorical data are based on optimizing a single objective function. However, a single objective function is often not applicable for different kinds of categorical data sets. Motivated by this fact, in this article, the categorical data clustering problem has been modeled as a multiobjective optimization problem. A popular multiobjective genetic algorithm has been used in this regard to optimize two objectives simultaneously, thus generating a set of non-dominated solutions. The performance of the proposed algorithm has been compared with that of different well known categorical data clustering algorithms and demonstrated for a variety of synthetic and real life categorical data sets. Also a statistical significance test has been performed to establish the superiority of the proposed algorithm.