Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has spread globally, and the number of worldwide cases continues to rise. The zoonotic origins of SARS-CoV-2 and its intermediate and potential spillback host reservoirs, besides humans, remain largely unknown. Because of ethical and experimental constraints and more important, to reduce and refine animal experimentation, we used our repository of well-differentiated airway epithelial cell (AEC) cultures from various domesticated and wildlife animal species to assess their susceptibility to SARS-CoV-2. We observed that SARS-CoV-2 replicated efficiently only in monkey and cat AEC culture models. Whole-genome sequencing of progeny viruses revealed no obvious signs of nucleotide transitions required for SARS-CoV-2 to productively infect monkey and cat AEC cultures. Our findings, together with previous reports of human-to-animal spillover events, warrant close surveillance to determine the potential role of cats, monkeys, and closely related species as spillback reservoirs for SARS-CoV-2.