Poxviruses are dsDNA viruses infecting a wide range of cell types, where they need to contend with multiple host antiviral pathways, including DNA and RNA sensing. Accordingly, poxviruses encode a variety of immune antagonists, most of which are expressed early during infection from within virus cores before uncoating and genome release take place. Amongst these antagonists, the poxvirus immune nuclease (poxin) counteracts the cyclic 2'3'-GMP-AMP (2'3'-cGAMP) synthase (cGAS)/stimulator of interferon genes DNA sensing pathway by degrading the immunomodulatory cyclic dinucleotide 2'3'-cGAMP, the product of activated cGAS. Here, we use poxviruses engineered to lack poxin to investigate how virus infection triggers the activation of STING and its downstream transcription factor interferon-responsive factor 3 (IRF3). Our results demonstrate that poxin-deficient vaccinia virus (VACV) and ectromelia virus (ECTV) induce IRF3 activation in primary fibroblasts and differentiated macrophages, although to a lower extent in VACV compared to ECTV. In fibroblasts, IRF3 activation was detectable at 10 h post-infection (hpi) and was abolished by the DNA replication inhibitor cytosine arabinoside (AraC), indicating that the sensing was mediated by replicated genomes. In macrophages, IRF3 activation was detectable at 4 hpi, and this was not affected by AraC, suggesting that the sensing in this cell type was induced by genomes released from incoming virions. In agreement with this, macrophages expressing short hairpin RNA (shRNA) against the virus uncoating factor D5 showed reduced IRF3 activation upon infection. Collectively, our data show that the viral genome is sensed by cGAS prior to and during genome replication, but immune activation downstream of it is effectively suppressed by poxin. Our data also support the model where virus uncoating acts as an immune evasion strategy to simultaneously cloak the viral genome and allow the expression of early immune antagonists.