Influenza A viruses are human pathogens with limited therapeutic options. Therefore, it is crucial to devise strategies for the identification of new classes of antiviral medications. The influenza A virus genome is constituted of 8 RNA segments. Two of these viral RNAs are transcribed into mRNAs that are alternatively spliced. The M1 mRNA encodes the M1 protein but is also alternatively spliced to yield the M2 mRNA during infection. M1 to M2 mRNA splicing occurs at nuclear speckles, and M1 and M2 mRNAs are exported to the cytoplasm for translation. M1 and M2 proteins are critical for viral trafficking, assembly, and budding. Here we show that gene knockout of the cellular protein NS1-BP, a constituent of the M mRNA speckle-export pathway and a binding partner of the virulence factor NS1 protein, inhibits M mRNA nuclear export without altering bulk cellular mRNA export, providing an avenue to preferentially target influenza virus. We performed a high-content, image-based chemical screen using single-molecule RNA-FISH to label viral M mRNAs followed by multistep quantitative approaches to assess cellular mRNA and cell toxicity. We identified inhibitors of viral mRNA biogenesis and nuclear export that exhibited no significant activity towards bulk cellular mRNA at non-cytotoxic concentrations. Among the hits is a small molecule that preferentially inhibits nuclear export of a subset of viral and cellular mRNAs without altering bulk cellular mRNA export. These findings underscore specific nuclear export requirements for viral mRNAs and phenocopy down-regulation of the mRNA export factor UAP56. This RNA export inhibitor impaired replication of diverse influenza A virus strains at non-toxic concentrations. Thus, this screening strategy yielded compounds that alone or in combination may serve as leads to new ways of treating influenza virus infection and are novel tools for studying viral RNA trafficking in the nucleus.