A MEMS pressure transducer includes a semiconductor body, a lower dielectric region arranged above the semiconductor body, and a fixed electrode region and a lower anchoring region, which are formed by conductive material, are arranged on the lower dielectric region and are laterally separated from each other. A membrane of conductive material is suspended above the fixed electrode region so as to delimit a cavity upwardly, the fixed electrode region facing the cavity, the membrane being deformable as a function of pressure and forming a variable capacitor together with the fixed electrode region. An upper anchoring region of conductive material laterally delimits the cavity and is interposed, in direct contact, between the membrane and the lower anchoring region.