Influenza A virus (IAV) infection of the respiratory tract can cause both respiratory and non-respiratory symptoms. Gastrointestinal (GI) symptoms such as diarrhea, vomiting, and abdominal pain can occur in persons with seasonal influenza A or novel IAV infections, but the extent to which IAVs can infect and replicate in GI tissues is understudied. The ongoing outbreak of A(H5N1) IAV in US dairy cattle associated with sporadic human infections has highlighted the potential public health threat posed by the introduction of infectious virus into materials that may be consumed by humans, such as milk. Here, we review epidemiologic reports documenting the frequency of GI complications in humans infected with seasonal and novel IAVs and present laboratory studies supporting the capacity of IAV to replicate in mammalian GI tissues, with an emphasis on A(H5N1) viruses. Studies assessing the ability of IAV to cause mammalian infection following consumption of virus-containing material are also presented. Collectively, these studies suggest that gastric exposure represents a potential non-respiratory route for A(H5N1) IAVs in mammals that can lead to infection and support that IAV may be detected in mammalian intestinal tissues following multiple exposure routes.