The present invention provides a modular prosthetic valve device designed as two or more device modules that may be delivered to a body lumen unassembled and then assembled into the assembled valve device in the body at least in part using a self-assembly member at or near the site of valve implantation. The device modules may include a support structure and a valve module. The valve module may be delivered in an unassembled, folded delivery configuration, and unfolded and assembled into a working configuration via the self-assembly member. In its unassembled form, the valve module may be a single-piece leaflets substructure or a plurality of valve sections. The self-assembly member has a delivery configuration and a preset configuration, and may be triggered to revert to the preset configuration to assemble the valve module. The modular valve device may be folded in a manner not possible with current valve devices, for example, by rolling the unassembled valve module along its circumferential axis in the direction of its height, so that the diameter of the folded valve module may be equivalent to that of one rolled leaflet. This feature of the invention provides a percutaneous valve device having a smaller delivery diameter than pre-assembled valve devices. This in turn permits use of a delivery device of reduced diameter and increases the flexibility of the loaded delivery device compared to percutaneous valve devices in the art. The invention further provides a system for and method of folding and delivering such a modular valve device and assembling it using the self-assembly member, preferably in the body.