As with other viral pathogens, HIV-1 and dengue virus (DENV) are dependent on their hosts for the bulk of the functions necessary for viral survival and replication. Thus, successful infection depends on the pathogen's ability to manipulate the biological pathways and processes of the organism it infects, while avoiding elimination by the immune system. Protein-protein interactions are one avenue through which viruses can connect with and exploit these host cellular pathways and processes. We developed a computational approach to predict interactions between HIV and human proteins based on structural similarity of 9 HIV-1 proteins to human proteins having known interactions. Using functional data from RNAi studies as a filter, we generated over 2,000 interaction predictions between HIV proteins and 406 unique human proteins. Additional filtering based on Gene Ontology cellular component annotation reduced the number of predictions to 502 interactions involving 137 human proteins. We find numerous known interactions as well as novel interactions showing significant functional relevance based on supporting Gene Ontology and literature evidence. We then applied this approach to predict interactions between (DENV) and both of its hosts, Homo sapiens and the insect vector Aedes aegypti. We predict over 4,000 interactions between DENV and humans, as well as 176 interactions between DENV and A. aegypti. Additional filtering based on shared Gene Ontology cellular component annotation reduced the number of predictions to approximately 2,000 for humans and 18 for A. aegypti. Of 19 experimentally validated interactions between DENV and humans extracted from the literature, this method was able to predict nearly half. Our results suggest specific interactions between virus and host proteins relevant to interferon signaling, transcriptional regulation, stress, and the unfolded protein response. Viruses manipulate cellular processes to their advantage through specific interactions with the host's protein interaction network. The interaction networks presented here provide a set of hypothesis for further experimental investigation into viral life cycles and potential therapeutic targets.