Influenza A viruses are a One Health threat because they can spill over between host populations, including among humans, swine, and birds. Surveillance of swine influenza virus in Hanoi, Vietnam, during 2013–2019 revealed gene pool enrichment from imported swine from Asia and North America and showed long-term maintenance, persistence, and reassortment of virus lineages. Genome sequencing showed continuous enrichment of H1 and H3 diversity through repeat introduction of human virus variants and swine influenza viruses endemic in other countries. In particular, the North American H1-δ1a strain, which has a triple-reassortant backbone that potentially results in increased human adaptation, emerged as a virus that could pose a zoonotic threat. Co-circulation of H1-δ1a viruses with other swine influenza virus genotypes raises concerns for both human and animal health.