Influenza is one of the most prevalent causes of death worldwide. Influenza A viruses (IAVs) naturally infect various avian and mammalian hosts, causing seasonal epidemics and periodic pandemics with high morbidity and mortality. The recent SARS-CoV-2 pandemic showed how an animal virus strain could unpredictably acquire the ability to infect humans with high infection transmissibility. Importantly, highly pathogenic avian influenza A viruses (AIVs) may cause human infections with exceptionally high mortality. Because these latter infections pose a pandemic potential, analyzing the ecology and evolution features of host expansion helps to identify new broad-range therapeutic strategies. Although IAVs are the prototypic example of molecular strategies that capitalize on their coding potential, the outcome of infection depends strictly on the complex interactions between viral and host cell factors. Most of the studies have focused on the influenza virus, while the contribution of host factors remains largely unknown. Therefore, a comprehensive understanding of mammals’ host response to AIV infection is crucial. This review sheds light on the involvement of the cellular cytoskeleton during the highly pathogenic AIV infection of mammalian hosts, allowing a better understanding of its modulatory role, which may be relevant to therapeutic interventions for fatal disease prevention and pandemic management.