A process for manufacturing MEMS devices, includes forming a first assembly, which comprises: a dielectric region; a redistribution region; and a plurality of unit portions. Each unit portion of the first assembly includes: a die arranged in the dielectric region; and a plurality of first and second connection elements, which extend to opposite faces of the redistribution region and are connected together by paths that extend in the redistribution region, the first connection elements being coupled to the die. The process further includes: forming a second assembly which comprises a plurality of respective unit portions, each of which includes a semiconductor portion and third connection elements; mechanically coupling the first and second assemblies so as to connect the third connection elements to corresponding second connection elements; and then removing at least part of the semiconductor portion of each unit portion of the second assembly, thus forming corresponding membranes.