Water Infrastructure (WI) is one of the most important sectors of Critical Infrastructure (CI); it encompasses drinking water, wastewater, and stormwater. The WI is vulnerable to the effects of Climate Change (CC) that can disrupt its functionality; thus, it needs to be adapted to CC, especially in the Mediterranean region, where these effects are expected to intensify during the twenty-first century. For this adaptation a Climate Risk and Vulnerability Assessment (CRVA) is required in the development of WI to identify the important climate hazards and to recommend the required measures for the adaptation of the WI to these hazards. In the present work, a CRVA methodology is developed and presented based on a literature survey and the relevant European Commission guidelines; it is structured around five key steps: (1) Description of the WI, (2) Climate change assessment, (3) Vulnerability assessment, (4) Risk assessment, and (5) Assessment of adaptation measures. The application of the methodology is illustrated indicatively to a wastewater system in Greece for which preliminary estimations are performed, results are discussed, and conclusions are drawn. The proposed methodology can be modified for application to other sectors of CI; moreover, is a valuable resource in academic curricula and ongoing research initiatives.