Porcine circovirus 3 (PCV3) infections cause clinical diseases similar to those seen in porcine circovirus 2 (PCV2) infections. It is unclear whether PCV3 infections can also cause immunosuppression like that seen with PCV2. Here, we report that Cap inhibits DNA-induced IFN-β mRNA transcription and IFN promoter activation. Cap was also found to inhibit cyclic GMP-AMP (cGAMP) synthase (cGAS) binding to interferon-stimulating DNA (ISD). Immunoprecipitation and mass spectrometry were used to identify cellular interaction partners of Cap. Cap interacted with G3BP1 and inhibited the interaction between GTPase-activating protein-(SH3 domain)-binding protein 1 (G3BP1) and cGAS. Furthermore, the destruction of endogenously expressed G3BP1 by siRNA significantly reduced IFN promoter activation, and phosphorylation of tank-binding kinase 1 (TBK1) was induced by ISD. Overexpression of G3BP1 attenuated the inhibition of ISD binding of cGAS by Cap and promoted phosphorylation of TBK1 and IRF3 induced by ISD. Collectively, our results show that the interaction between Cap and G3BP1 prevents cGAS from recognizing DNA, thereby inhibiting the IFN production.