Hollow fibers find useful applications in different disciplines like fluid transport and purification, optical guidance, and composite reinforcement. In tissue engineering, they can be used to direct tissue in-growth or to serve as drug delivery depots. The fabrication techniques currently available, however, do not allow to simultaneously organize them into three-dimensional (3D) matrices, thus adding further functionality to approach more complicated or hierarchical structures. We report here the development of a novel technology to fabricate hollow fibers with controllable hollow cavity diameter and shell thickness. By exploiting viscous encapsulation, a rheological phenomenon often undesired in molten polymeric blends flowing through narrow ducts, fibers with a shell-core configuration can be extruded. Hollow fibers are then obtained by selective dissolution of the inner core polymer. The hollow cavity diameter and the shell thickness can be controlled by varying the polymers in the blend, the blend composition, and the extrusion nozzle diameter. Simultaneous with extrusion, the extrudates are organized into 3D matrices with different architectures and custom-made shapes by 3D fiber deposition, a rapid prototyping tool which has recently been applied for the production of scaffolds for tissue engineering purposes. Applications in tissue engineering and controlled drug delivery of these constructs are presented and discussed.