The herpes simplex virus virion host shutoff (vhs) RNase destabilizes cellular and viral mRNAs and blunts host innate antiviral responses. Previous work demonstrated that cells infected with vhs mutants display enhanced activation of the host double-stranded RNA (dsRNA)-activated protein kinase R (PKR), implying that vhs limits dsRNA accumulation in infected cells. Confirming this hypothesis, we show that partially complementary transcripts of the UL23/UL24 and UL30/31 regions of the viral genome increase in abundance when vhs is inactivated, giving rise to greatly increased levels of intracellular dsRNA formed by annealing of the overlapping portions of these RNAs. Thus, vhs limits accumulation of dsRNA at least in part by reducing the levels of complementary viral transcripts. We then asked if vhs also destabilizes dsRNA after its initial formation. Here, we used a reporter system employing two mCherry expression plasmids bearing complementary 3' UTRs to produce defined dsRNA species in uninfected cells. The dsRNAs are unstable, but are markedly stabilized by co-expressing the HSV dsRNA-binding protein US11. Strikingly, vhs delivered by super-infecting HSV virions accelerates the decay of these pre-formed dsRNAs in both the presence and absence of US11, a novel and unanticipated activity of vhs. Vhs binds the host RNA helicase eIF4A, and we find that vhs-induced dsRNA decay is attenuated by the eIF4A inhibitor hippuristanol, providing evidence that eIF4A participates in the process. Our results show that a herpesvirus host shutoff RNase destabilizes dsRNA in addition to targeting partially complementary viral mRNAs, raising the possibility that the mRNA destabilizing proteins of other viral pathogens dampen the host response to dsRNA through similar mechanisms.