The Type VI secretion system (T6SS) is a bacterial nanomachine that delivers toxic effectors to kill competitors or subvert some of their key functions. Here, we use transposon directed insertion-site sequencing to identify T6SS toxins associated with the H1-T6SS, one of the three T6SS machines found in Pseudomonas aeruginosa. This approach identified several putative toxin-immunity pairs, including Tse8-Tsi8. Full characterization of this protein pair demonstrated that Tse8 is delivered by the VgrG1a spike complex into prey cells where it targets the transamidosome, a multiprotein complex involved in protein synthesis in bacteria that lack either one, or both, of the asparagine and glutamine transfer RNA synthases. Biochemical characterization of the interactions between Tse8 and the transamidosome components GatA, GatB and GatC suggests that the presence of Tse8 alters the fine-tuned stoichiometry of the transamidosome complex, and in vivo assays demonstrate that Tse8 limits the ability of prey cells to synthesize proteins. These data expand the range of cellular components targeted by the T6SS by identifying a T6SS toxin affecting protein synthesis and validate the use of a transposon directed insertion site sequencing-based global genomics approach to expand the repertoire of T6SS toxins in T6SS-encoding bacteria.