A pressure-sensor device (1) comprises: a pressure-sensitive component (5, 5a, 6), having a sensor body (5) that includes an elastically deformable membrane part (5a) and at least one detection element (6) suitable for detecting a deformation of the membrane part (5a); a supporting structure (2, 3) for supporting the pressure-sensitive component (5, 5a, 6), having a passageway (15) for a fluid of which a pressure is to be measured. The supporting structure (2, 3) comprises: a supporting body (2) with respect to which the sensor body (5) is positioned in such a way that its membrane part (5a) is exposed to the fluid exiting the passageway (15), the supporting body (2) having at least one through cavity (14), a compressible body (16), which is configured for compensating possible variations of volume of the fluid. The supporting body (2) has a first body portion (2c) comprising a transverse wall (22) of the through cavity (14), defined in which is at least one first passage (23a-23b) and at least one second passage (24), the at least one first passage (23a-23b) belonging to the passageway (15) for the fluid. The compressible body (16) is an element over-moulded with respect to the supporting body (2), that has respective opposite portions (20, 21) which extend in positions corresponding to opposite sides of the transverse wall (22), and which are connected to one another via at least one intermediate portion (16a) of the compressible body (16) that that extends through the at least one second passage (24). The first body portion (2c) is shaped to define at least one step or one projection or one relief (25; 28) which determines at least one of: a cross-sectional narrowing of the at least one second passage (24), configured to define a corresponding cross-sectional reduction of the at least one intermediate portion (16a) of the compressible body (16), and a development of the at least one intermediate portion (16a) of the compressible body (16) which is generally tortuous or comprises a number of stretches substantially angled to each other.