Influenza viruses are the cause of yearly epidemics and occasional pandemics that represent a significant challenge to public health. Current control strategies are imperfect and there is an unmet need for new antiviral therapies. Here, we report the identification of small molecule compounds able to effectively and specifically inhibit growth of influenza A and B viruses in cultured cells through targeting an assembly interface of the viral RNA-dependent RNA polymerase. Using an existing crystal structure of the primary protein–protein interface between the PB1 and PA subunits of the influenza A virus polymerase, we conducted an in silico screen to identify potential small molecule inhibitors. Selected compounds were then screened for their ability to inhibit the interaction between PB1 and PA in vitro using an ELISA-based assay and in cells, to inhibit nuclear import of a binary PB1–PA complex as well as transcription by the full viral ribonucleoprotein complex. Two compounds emerged as effective inhibitors with IC ₅₀ values in the low micromolar range and negligible cytotoxicity. Of these, one compound also acted as a potent replication inhibitor of a variety of influenza A virus strains in Madin-Darby canine kidney (MDCK) cells, including H3N2 and H1N1 seasonal and 2009 pandemic strains. Importantly, this included an oseltamivir-resistant isolate. Furthermore, potent inhibition of influenza B viruses but not other RNA or DNA viruses was seen. Overall, these compounds provide a foundation for the development of a new generation of therapeutic agents exhibiting high specificity to influenza A and B viruses.