In the last few years there has been an impressive growth of connections between medicine and artificial intelligence (AI) that have been characterized by the specific focus on single problems along with corresponding clinical data. This paper proposes a new perspective in which the focus is on the progressive accumulation of a universal repository of clinical hyperlinked data in the spirit that gave rise to the birth of the Web. The underlining idea is that this repository, that is referred to as the Web of Clinical Data (WCD), will dramatically change the AI approach to medicine and its effectiveness. It is claimed that research and AI-based applications will undergo an evolution process that will likely reinforce systematically the solutions implemented in medical apps made available in the WCD. The distinctive architectural feature of the WCD is that this universal repository will be under control of clinical units and hospitals, which is claimed to be the natural context for dealing with the critical issues of clinical data.