Human Carbonic Anhydrase (hCA) IX is a membrane-associated member of the CA enzyme family, involved in solid tumor acidification. This enzyme is a marker of tumor hypoxia and a prognostic factor for several human cancers. In a recent paper, we showed that CA IX interacts with cullin-associated NEDD8-dissociated protein 1 (CAND1), a nuclear protein involved in gene transcription and assembly of SCF ubiquitin ligase complexes. A functional role for this interaction was also identified, since lower CA IX levels were observed in cells with decreased CAND1 expression via shRNA-mediated interference. In this paper, we describe the identification of the structural determinants responsible for the CA IX/CAND1 interaction by means of a multidisciplinary approach, consisting of binding assay measurements, molecular docking, and site-directed mutagenesis. These data open a novel scenario in the design of anticancer drugs targeting CA IX. Indeed, the knowledge of the structural determinants responsible for the CAND1/CA IX interaction provides the molecular basis to design molecules able to destabilize it. Due to the proposed function of CAND1 in stabilizing CA IX, these molecules could represent an efficient tool to lower the amount of CA IX in hypoxic cancer cells, thus limiting its action in survival and the metastatic spread of tumors.