A main requirement for the Future Internet is to enable self-management behaviors facilitating the network to adapt to changing conditions and self-heal in the face of erroneous states. On the basis of Autonomic Fault-Management principles, this paper proposes a framework consisting of a set of components operating inside the network elements and allowing the devices to collaboratively realize self-healing. In that context, Autonomic Fault-Management is intuitively constituted by the detection of the presence of faulty conditions, followed in turn by the self-diagnosis and identification of the corresponding root causes, and completed consequently by the removal of the identified root causes and their effects. The proposed framework implements a distributed control loop that interacts with the network operations personnel in case the current erroneous state is not resolvable by means of Autonomic Fault-Management. We argue that there are a number of mutual benefits between our proposed framework and the IPv6 protocol suite. This is demonstrated by a case study that illustrates these benefits and shows how the capabilities of IPv6 can be enhanced through the self-healing mechanisms of the proposed framework. Finally, the prototype implementation used for the case study is analyzed in terms of scalability and overhead produced in the network nodes