A process for manufacturing a MEMS pressure sensor having a micromechanical structure comprising: providing a wafer including a substrate of semiconductor material and having a top surface; forming a cavity within said substrate and a membrane suspended above said cavity; forming a fluidic-communication access (22; 37), for fluidic communication of said membrane with an external environment, set at a pressure the value of which has to be determined; forming, suspended above said membrane, a plate region, made of conductive material, separated from said membrane by an empty space; and forming electrical-contact elements (30a, 30b), for electrical connection of said membrane and said plate region, which are designed to form the plates of a sensing capacitor, the value of capacitance of which is indicative of the value of pressure to be detected, characterized in that forming the cavity includes forming a buried cavity entirely contained within said substrate and separated from the top surface by said membrane, which is also formed within said substrate, and in that forming a plate region comprises, after formation of said buried cavity, the steps of: forming a sacrificial layer on the top surface of said substrate; forming a conductive layer on the sacrificial layer; opening a number of holes through said conductive layer, in a position vertically corresponding to said membrane; and partially removing said sacrificial layer through said holes so as to release said conductive layer with respect to the substrate, to form said plate region and said empty space above said membrane. providing a wafer including a substrate of semiconductor material and having a top surface; forming a cavity within said substrate and a membrane suspended above said cavity; forming a fluidic-communication access (22; 37), for fluidic communication of said membrane with an external environment, set at a pressure the value of which has to be determined; forming, suspended above said membrane, a plate region, made of conductive material, separated from said membrane by an empty space; and forming electrical-contact elements (30a, 30b), for electrical connection of said membrane and said plate region, which are designed to form the plates of a sensing capacitor, the value of capacitance of which is indicative of the value of pressure to be detected, characterized in that forming the cavity includes forming a buried cavity entirely contained within said substrate and separated from the top surface by said membrane, which is also formed within said substrate, and in that forming a plate region comprises, after formation of said buried cavity, the steps of: forming a sacrificial layer on the top surface of said substrate; forming a conductive layer on the sacrificial layer; opening a number of holes through said conductive layer, in a position vertically corresponding to said membrane; and partially removing said sacrificial layer through said holes so as to release said conductive layer with respect to the substrate, to form said plate region and said empty space above said membrane. forming a sacrificial layer on the top surface of said substrate; forming a conductive layer on the sacrificial layer; opening a number of holes through said conductive layer, in a position vertically corresponding to said membrane; and partially removing said sacrificial layer through said holes so as to release said conductive layer with respect to the substrate, to form said plate region and said empty space above said membrane.