The human genome is organized into topologically associating domains (TADs), which represent contiguous regions with a higher frequency of intra-interactions as opposed to inter-interactions. TADs contribute to gene expression regulation by restricting interactions between regulatory elements, and their disruption by genomic rearrangements can result in altered gene expression and, ultimately, in cancer. Here, we provide a proof-of-principle that mutations within TADs can be used to predict the survival of cancer patients. For this purpose, we first constructed a set of 1,467 TADs representing the three-dimensional organization of genome across 24 normal human tissues. We then used Cox regression analysis to assess the prognostic value of the TADs in different cancer types, and identified a total of 35 TADs that were prognostic for at least one of nine cancer types. Interestingly, only 46% of the prognostic TADs comprised one or more genes with a known causal association with cancer. Moreover, for those TADs encompassing such a gene, the prognostic effect of the TAD was only directed related to the presence/absence of mutations in the gene in 13% of the cases. These observations indicate that the predictive power of a large proportion of the prognostic TADs is independent of whether pan-cancer genes are mutated or not. Furthermore, 34% of the 35 prognostic TADs showed strong structural perturbations in the cancer genome, which might mediate cancer development and progression. This study has important implications for the interpretation of cancer-related non-coding mutations and offer insights to new strategies for personalizing cancer medicine.