Klebsiella species are able to colonize a wide range of environments and include daunting nosocomial pathogens. Here, we sought to determine the abundance and infectivity of prophages of Klebsiella to understand how the interactions between induced prophages and bacteria affect population dynamics and evolution. We identified many prophages in the species, placing these taxa among the top 5% of the most polylysogenic bacteria. We selected 35 representative strains of Klebsiella to establish a network of induced phage-bacteria interactions. This revealed that many prophages are able to enter the lytic cycle, and subsequently kill or lysogenize closely-related Klebsiella strains. Although 60% of the tested strains could produce phages that infect at least one other strain, the interaction network of all pairwise cross-infections is very sparse, most interactions are null, and is modular because of the capsule serotype. Capsule mutants remain uninfected showing that the capsule is required for successful infection. Accordingly, experiments where bacteria are predated by their own prophages result in accelerated loss of the capsule. Our results show that infectiousness defines interaction modules between small subsets of phages and bacteria in function of capsule serotype. This limits the role of prophages as competitive weapons because they can infect very few strains of the species. This should also restrict phage-driven gene flow across the species. However, if capsule loss driven by phage predation is followed by the acquisition of a novel capsule, then bacteria shift to another module where they can be infected by other phages that can transduce genes from other bacterial strains.