Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the third highly pathogenic coronavirus to spill over to humans in less than 20 years, after SARS-CoV-1 in 2002-2003 and Middle East respiratory syndrome (MERS)-CoV in 2012. SARS-CoV-2 is the etiologic agent of coronavirus disease 19 (COVID-19), which ranges from mild respiratory symptoms to severe lung injury and death in the most severe cases. The COVID-19 pandemic is currently a major health issue worldwide. Immune dysregulation characterized by altered innate cytokine responses is thought to contribute to the pathology of COVID-19 patients, which is a testimony of the fundamental role of the innate immune response against SARS-CoV-2. Here, we further characterized the host cell antiviral response against SARS-CoV-2 by using primary human airway epithelia and immortalized model cell lines. We mainly focused on the type I and III interferon (IFN) responses, which lead to the establishment of an antiviral state through the expression of IFN-stimulated genes (ISGs). Our results demonstrate that both primary airway epithelial cells and model cell lines elicit a robust immune response characterized by a strong induction of type I and III IFN through the detection of viral pathogen molecular patterns (PAMPs) by melanoma differentiation associated gene (MDA)-5. However, despite the high levels of type I and III IFNs produced in response to SARS-CoV-2 infection, the IFN response was unable to control viral replication, whereas IFN pre-treatment strongly inhibited viral replication and de novo production of infectious virions. Taken together, these results highlight the complex and ambiguous interplay between viral replication and the timing of IFN responses.