Respiratory epithelial cells and macrophages are the key innate immune cells that play an important role in the pathogenesis of influenza A virus infection. We found that these two cell types from both human and pig showed comparable susceptibilities to initial infection with a highly pathogenic avian influenza (HPAI) H5N1 virus (A/turkey/Turkey/1/05) and a moderately pathogenic human influenza H1N1 virus (A/USSR/77), but there were contrasting differences in host innate immune responses. Human cells mounted vigorous cytokine (tumor necrosis factor alpha [TNF-α] and interleukin-6 [IL-6]) and chemokine (CXCL9, CXCL10, and CXCL11) responses to H5N1 virus infection. However, pig epithelial cells and macrophages showed weak or no TNF-α and chemokine induction with the same infections. The apparent lack of a strong proinflammatory response, corroborated by the absence of TNF-α induction in H5N1 virus-challenged pigs, coincided with greater cell death and the reduced release of infectious virus from infected pig epithelial cells. Suppressor of cytokine signaling 3 (SOCS3), a protein suppressor of the JAK-STAT pathway, was constitutively highly expressed and transcriptionally upregulated in H5N1 virus-infected pig epithelial cells and macrophages, in contrast to the corresponding human cells. The overexpression of SOCS3 in infected human macrophages dampened TNF-α induction. In summary, we found that the reported low susceptibility of pigs to contemporary Eurasian HPAI H5N1 virus infections coincides at the level of innate immunity of respiratory epithelial cells and macrophages with a reduced output of viable virus and an attenuated proinflammatory response, possibly mediated in part by SOCS3, which could serve as a target in the treatment or prevention of virus-induced hypercytokinemia, as observed for humans.