Change-point models deal with ordered data sequences. Their primary goal is to infer the locations where an aspect of the data sequence changes. In this paper, we propose and implement a nonparametric Bayesian model for clustering observations based on their constant-wise change-point profiles via Gibbs sampler. Our model incorporates a Dirichlet Process on the constant-wise change-point structures to cluster observations while simultaneously performing multiple change-point estimation. Additionally, our approach controls the number of clusters in the model, not requiring the specification of the number of clusters a priori. Satisfactory clustering and estimation results were obtained when evaluating our method under various simulated scenarios and on a real dataset from single-cell genomic sequencing. Our proposed methodology is implemented as an R package called BayesCPclust and is available from the Comprehensive R Archive Network at https://CRAN.R-project.org/package=BayesCPclust.