Cellular antiviral programs encode molecules capable of targeting multiple steps in the virus lifecycle. Zinc-finger antiviral protein (ZAP) is a central and general regulator of antiviral activity that targets pathogen mRNA stability and translation. ZAP is diffusely cytoplasmic, but upon infection ZAP is targeted to particular cytoplasmic structures, termed stress granules (SGs). However, it remains unclear if ZAP's antiviral activity correlates with SG localization, and what molecular cues are required to induce this localization event. Here, we use Sindbis virus (SINV) as a model infection and find that ZAP's localization to SGs can be transient. Sometimes no apparent viral infection follows ZAP SG localization but ZAP SG localization always precedes accumulation of SINV non-structural protein, suggesting virus replication processes trigger SG formation and ZAP recruitment. Data from single-molecule RNA FISH corroborates this finding as the majority of cells with ZAP localization in SGs contain low levels of viral RNA. Furthermore, ZAP recruitment to SGs occurred in ZAP-expressing cells when co-cultured with cells replicating full-length SINV, but not when co-cultured with cells replicating a SINV replicon. ZAP recruitment to SGs is functionally important as a panel of alanine ZAP mutants indicate that the anti-SINV activity is correlated with ZAP's ability to localize to SGs. As ZAP is a central component of the cellular antiviral programs, these data provide further evidence that SGs are an important cytoplasmic antiviral hub. These findings provide insight into how antiviral components are regulated upon virus infection to inhibit virus spread.