We consider a multivariate setting with q categorical variables and observations collected on n individuals. Our objective is to cluster these data into groups characterized by homogeneous dependence structures among variables. We consider undirected graphs as a multivariate tool to model dependence relations between variables. For clustering purposes, we develop a Bayesian non-parametric mixture of categorical graphical models based on a Dirichlet Process prior. We provide full Bayesian inference for the model and develop a Markov Chain Monte Carlo strategy for posterior estimation of clustering and graphical structures characterizing cluster-specific dependence relations.