The novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus responsible for the current COVID-19 pandemic and has now infected more than 200 million people with more than 4 million deaths globally. Recent data suggest that symptoms and general malaise may continue long after the infection has ended in recovered patients, suggesting that SARS-CoV-2 infection has profound consequences in the host cells. Here we report that SARS-CoV-2 infection can trigger a DNA damage response (DDR) in African green monkey kidney cells (Vero E6). We observed a transcriptional upregulation of the Ataxia telangiectasia and Rad3 related protein (ATR) in infected cells. In addition, we observed enhanced phosphorylation of CHK1, a downstream effector of the ATR DNA damage response, as well as H2AX. Strikingly, SARS-CoV-2 infection lowered the expression of TRF2 shelterin-protein complex, and reduced telomere lengths in infected Vero E6 cells. Thus, our observations suggest SARS-CoV-2 may have pathological consequences to host cells beyond evoking an immunopathogenic immune response.