Cas13a has been used to target RNA viruses in cell culture, but efficacy has not been demonstrated in animal models. In this study, we used messenger RNA (mRNA)-encoded Cas13a for mitigating influenza virus A and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection in mice and hamsters, respectively. We designed CRISPR RNAs (crRNAs) specific for PB1 and highly conserved regions of PB2 of influenza virus, and against the replicase and nucleocapsid genes of SARS-CoV-2, and selected the crRNAs that reduced viral RNA levels most efficiently in cell culture. We delivered polymer-formulated Cas13a mRNA and the validated guides to the respiratory tract using a nebulizer. In mice, Cas13a degraded influenza RNA in lung tissue efficiently when delivered after infection, whereas in hamsters, Cas13a delivery reduced SARS-CoV-2 replication and reduced symptoms. Our findings suggest that Cas13a-mediated targeting of pathogenic viruses can mitigate respiratory infections.