A micromechanical structure for a MEMS capacitive acoustic transducer, has: a substrate made of semiconductor material, having a front surface lying in a horizontal plane; a membrane, coupled to the substrate and designed to undergo deformation in the presence of incident acoustic-pressure waves; a fixed electrode, which is rigid with respect to the acoustic-pressure waves and is coupled to the substrate by means of an anchorage structure, in a suspended position facing the membrane to form a detection capacitor. The anchorage structure has at least one pillar element, which is at least in part distinct from the fixed electrode and supports the fixed electrode in a position parallel to the horizontal plane.