Spillovers of zoonotic Influenza A viruses (IAVs) into farmed animals and humans have the potential to trigger epidemics or even global pandemics. We introduce FluWarning, a highly efficient and elegant computational method based on anomaly detection of codon bias and dinucleotide composition for early identification of divergent viral HA segments. We applied FluWarning to the 2009 influenza pandemic as a test case. FluWarning successfully identified the emergence of pdm09, the virus that caused the pandemic, with warnings preceding the observed global spread. Applied to H5N1 specimens collected between 2019 and 2025, FluWarning flagged genotypes D1.1 and B3.13, both associated with recent spillovers in dairy cows in the United States. In summary, FluWarning is an effective, lightweight, multiscale warning system for IAVs, detecting spillovers with few available sequences.