SARS‐CoV‐2 is a newly emerged coronavirus, causing the global pandemic of respiratory coronavirus disease (COVID‐19). The type I interferon (IFN) pathway is of particular importance for anti‐viral defense and recent studies identified that type I IFNs drive early inflammatory responses to SARS‐CoV‐2. Here, we use a mouse model of SARS‐CoV‐2 infection, facilitating viral entry by intranasal recombinant Adeno‐Associated Virus (rAAV) transduction of hACE2 in wildtype (WT) and type I IFN receptor‐1 deficient (Ifnar1^–/–) mice, to study the role of type I IFN signalling and innate immune responses during SARS‐CoV‐2 infection. Our data show that type I IFN signalling is essential for inducing anti‐viral effector responses to SARS‐CoV‐2, control of virus replication, and to prevent enhanced disease. Furthermore, hACE2‐Ifnar1^–/– mice had increased gene expression of the chemokine Cxcl1 and airway infiltration of neutrophils as well as reduced and delayed production of monocyte‐recruiting chemokine CCL2. hACE2‐Ifnar1^–/– mice showed altered recruitment of inflammatory myeloid cells to the lung upon SARS‐CoV‐2 infection, with a shift from Ly6C⁺ to Ly6C^– expressing cells. Together, our findings suggest that type I IFN signalling deficiency results in a dysregulated innate immune response to SARS‐CoV‐2 infection.