Recent findings in permanent cell lines suggested that SARS-CoV-2 Omicron BA.1 induces a stronger interferon response than Delta. Here, we show that BA.1 and BA.5 but not Delta induce an antiviral state in air-liquid interface cultures of primary human bronchial epithelial cells and primary human monocytes. Both Omicron subvariants caused the production of biologically active types I (α/β) and III (λ) interferons and protected cells from super-infection with influenza A viruses. Notably, abortive Omicron infection of monocytes was sufficient to protect monocytes from influenza A virus infection. Interestingly, while influenza-like illnesses surged during the Delta wave in England, their spread rapidly declined upon the emergence of Omicron. Mechanistically, Omicron-induced interferon signaling was mediated via double-stranded RNA recognition by MDA5, as MDA5 knockout prevented it. The JAK/STAT inhibitor baricitinib inhibited the Omicron-mediated antiviral response, suggesting it is caused by MDA5-mediated interferon production, which activates interferon receptors that then trigger JAK/STAT signaling. In conclusion, our study (1) demonstrates that only Omicron but not Delta induces a substantial interferon response in physiologically relevant models, (2) shows that Omicron infection protects cells from influenza A virus super-infection, and (3) indicates that BA.1 and BA.5 induce comparable antiviral states.