Modified vaccinia Ankara (MVA) is an attenuated strain of vaccinia virus (VACV), a dsDNA virus that replicates its genome in the cytoplasm and as a result is canonically sensed by the cyclic GMP-AMP synthase (cGAS) and its downstream stimulator of interferon genes (STING). MVA has a highly restricted host range due to major deletions in its genome including inactivation of immunomodulatory genes, only being able to grow in avian cells and the hamster cell line BHK21. Here we studied the interplay between MVA and the cGAS/STING DNA in this permissive cell line and determined whether manipulation of this axis could impact MVA replication and cell responses. We demonstrate that BHK21 cells retain a functional cGAS/STING axis that responds to canonical DNA sensing agonists, upregulating interferon stimulated genes (ISGs). BHK21 cells also respond to MVA, but with a distinct ISG profile. This profile remains unaltered after CRISPR/Cas9 knock-out editing of STING and ablation of cytosolic DNA responses, indicating that MVA responses are independent of the cGAS/STING axis. Furthermore, infection by MVA diminishes the ability of BHK21 cells to respond to exogenous DNA suggesting that MVA still encodes uncharacterised inhibitors of DNA sensing. This suggests that using attenuated strains in permissive cell lines may assist in identification of novel host-virus interactions that may be of relevance to disease or the therapeutic applications of poxviruses.