An implantable flow restrictor device is disclosed for initially restricting, then gradually restoring blood flow through a body vessel after an interventional procedure. A self-expanding annular member having a constricted diameter gives the device a frustoconical configuration that reduces blood flow therethrough upon initial deployment at a treatment site. The annular member is constricted by a plurality of linkages that operate to allow the annular member to gradually expand, thereby transforming the flow restrictor device to a cylindrical configuration that allows unimpeded blood flow therethrough. In one embodiment, expansion of the annular member is achieved via biodegradation of the linkages. In another embodiment, expansion of the annular member is achieved via creep deformation of the linkages. The flow restrictor device may be attached to an endoluminal prosthesis, or may be a separate complementary component that is delivered during an interventional procedure.