Human herpesviruses are responsible for a range of debilitating acute and recurrent diseases, including a number of malignancies. Current treatments are limited to targeting the herpesvirus DNA polymerases, but with emerging viral resistance and little efficacy against the oncogenic herpesviruses, there is an urgent need for new antiviral strategies. Here, we describe a mechanism to inhibit the replication of the oncogenic herpesvirus Kaposi's sarcoma-associated herpesvirus (KSHV), by targeting the ATP-dependent formation of viral ribonucleoprotein particles (vRNPs). We demonstrate that small-molecule inhibitors which selectively inhibit the ATPase activity of the cellular human transcription/export complex (hTREX) protein UAP56 result in effective inhibition of vRNP formation, viral lytic replication and infectious virion production. Strikingly, as all human herpesviruses use conserved mRNA processing pathways involving hTREX components, we demonstrate the feasibility of this approach for pan-herpesvirus inhibition.