Zoonotic transmission of influenza A viruses can give rise to devastating pandemics, but currently it is impossible to predict the pandemic potential of circulating avian influenza viruses. Here, we describe a new mouse model suitable for such risk assessment, based on the observation that the innate restriction factor MxA represents an effective species barrier that must be overcome by zoonotic viruses. Our mouse lacks functional endogenous Mx genes but instead carries the human MX1 locus as a transgene. Such transgenic mice were largely resistant to highly pathogenic avian H5 and H7 influenza A viruses, but were almost as susceptible to infection with influenza viruses of human origin as nontransgenic littermates. Influenza A viruses that successfully established stable lineages in humans have acquired adaptive mutations which allow partial MxA escape. Accordingly, an engineered avian H7N7 influenza virus carrying a nucleoprotein with signature mutations typically found in human virus isolates was more virulent in transgenic mice than parental virus, demonstrating that a few amino acid changes in the viral target protein can mediate escape from MxA restriction in vivo. Similar mutations probably need to be acquired by emerging influenza A viruses before they can spread in the human population.