The E6 oncoprotein produced by high-risk mucosal HPV stimulates ubiquitinylation and proteasome-dependent degradation of the tumour suppressor p53 via formation of a trimeric complex comprising E6, p53, and E6-AP. p53 is also degraded by its main cellular regulator MDM2. The main binding site of p53 to MDM2 is situated in the natively unfolded N-terminal region of p53. By contrast, the regions of p53 implicated in the degradation by viral E6 are not fully identified to date. Here we generated a series of mutations (Y103G, Y107G, T155A, T155V, T155D, L264A, L265A) targeting the central folded core domain of p53 within a region opposite to its DNA-binding site. We analysed by in vitro and in vivo assays the impact of these mutations on p53 degradation mediated by viral E6 oncoprotein. Whereas all mutants remained susceptible to MDM2-mediated degradation, several of them (Y103G, Y107G, T155D, L265A) became resistant to E6-mediated degradation, confirming previous works that pointed to the core domain as an essential region for the degradation of p53. In parallel, we systematically checked the impact of the mutations on the transactivation activity of p53 as well as on the conformation of p53, analysed by Nuclear Magnetic Resonance (NMR), circular dichroism (CD), and antibody probing. These measurements suggested that the conformational integrity of the core domain is an essential parameter for the degradation of p53 by E6, while it is not essential for the degradation of p53 by MDM2. Thus, the intracellular stability of a protein may or may not rely on its biophysical stability depending on the degradation pathway taken into consideration.