In this paper we propose MCOV, a covariance-based descriptor for the fusion of shape and color information of 3D surfaces with associated texture aiming at a robust characterization and matching of areas in 3D point clouds. The proposed descriptor is based on the notion of covariance in order to create compact representations of the variations of texture and surface features in a radial neighbourhood, instead of using the absolute features themselves. Even if this representation is compact and low dimensional, it still offers discriminative power for complex scenes. The codification of feature variations in a close environment of a point provides invariance to rigid spatial transformations and robustness to changes in noise and scene resolution from a simple formulation perspective. Results on 3D points discrimination are validated by testing this approach performance on top of a selected database, corroborating the adequacy of our approach on the posed challenging conditions and outperforming other state-of-the-art 3D point descriptor methods. A qualitative test application on matching objects on scenes acquired with a common depth-sensor device is also provided.