Significance There is a strong need for the development of new antiviral therapies, and this study sheds light on a host–virus interaction that is significant for a number of medically important human viruses. The study also suggests that the RNA-binding zinc finger CCCH-type containing 11A (ZC3H11A) protein takes part in a mechanism that facilitates nuclear export of mRNA, particularly under cellular stress, a mechanism that has been “hijacked” by several nuclear-replicating viruses to promote their replication. ZC3H11A is therefore a potential target for development of an antiviral therapy.