Post-transcriptional regulation plays an important role in infection and immunity. Regulation of translation and mRNA stability allows tight control over potent responses by both the host and the invading virus. Here, we apply ribosome profiling to assess post-transcriptional regulation of host genes after 24 hours of SARS-CoV-2 infection in the human lung epithelial cell line (Calu-3). We show restriction of numerous transcription factors (JUN, ZBTB20, ATF3, HIVEP2 and EGR1) as well as select antiviral cytokine genes, namely IFNB1, IFNL1,2 and 3, IL-6 and CCL5, at the post-transcriptional level by SARS-CoV-2, consistent with the delayed IFN response seen in COVID19. Upstream open reading frames were not protective against translational down-regulation suggesting a mechanism independent of the integrated stress response. Unstable mRNAs were more sensitive to translational down-regulation, suggesting an early step such as nascent mRNA recruitment to the ribosome may be affected. We know that the SARS-CoV-2 Non-structural protein 1 (Nsp1) acts in this way. An early phase restriction of antiviral transcripts in the lungs may allow high viral load and consequent immune dysregulation typically seen in SARS-CoV-2 infection.