Mixture models are widely used in unsupervised machine learning applications where annotating a large amount of data is not feasible. They have succeeded in various real-world problems, including medical applications, human activity recognition, and anomaly detection. This paper proposes a fully Bayesian analysis of the multivariate McDonald's Beta mixture model (McDBMM) using Gibbs sampling method and Metropolis-Hastings to estimate parameters. In addition, we integrated a feature selection technique which simultaneously determines the most relevant features for our mixture model. This allows for the simultaneous selection of the most relevant features, improving the accuracy and efficiency of the unsupervised learning process. Our approach is evaluated on challenging applications, including lung cancer image analysis and human activity recognition. Experimental results indicate that our proposed method is an effective solution compared to the Gaussian mixture model (GMM).