The Janus kinase (JAK)–signal transducer and activator of transcription (STAT) signaling pathway plays a crucial role in innate immunity by inducing antiviral proteins in response to interferon signals. Marek’s disease virus (MDV), a member of the alpha-herpes virus family, exerts potent tumorigenic and immunosuppressive effects. Recent studies have primarily focused on the tumorigenic mechanisms of MDV, and the mechanism of immune evasion has not been fully understood. In this study, we showed that MDV reduced the production of interferon-stimulated gene (ISGs) by inhibiting the phosphorylation and nuclear translocation of STAT1. Using a dual-luciferase reporter system, we screened for viral proteins that significantly suppress interferon-stimulated response element (ISRE) promoter activity. Meq overexpression markedly reduced ISRE promoter activity and ISG expression, whereas infection with Meq-deficient MDV induced higher ISG production in vitro and in vivo than infection with wild-type MDV. Meq also inhibited the phosphorylation and nuclear translocation of STAT1. Further experiments showed that Meq interacted with JAK1 and tyrosine kinase 2 (TYK2) and thereby inhibited JAK1–STAT1 interactions. Meq degraded TYK2 via a caspase-mediated pathway. The Meq-deficient MDV mutant replicated less efficiently than the wild-type MDV, both in vitro and in vivo. Collectively, these findings demonstrate that Meq played an immunosuppressive role in MDV by attenuating the JAK–STAT signaling pathway, which facilitated escape from innate immune-surveillance mechanisms.