A process for manufacturing a micromechanical structure envisages: forming a buried cavity within a body of semiconductor material, separated from a top surface of the body by a first surface layer; and forming an access duct for fluid communication between the buried cavity and an external environment. The method envisages: forming an etching mask on the top surface at a first access area; forming a second surface layer on the top surface and on the etching mask; carrying out an etch such as to remove, in a position corresponding to the first access area, a portion of the second surface layer, and an underlying portion of the first surface layer not covered by the etching mask until the buried cavity is reached, thus forming both the first access duct and a filter element, set between the first access duct and the same buried cavity.