Host signaling pathways play important roles in the replication of influenza virus, but their functional effects remain to be characterized at the molecular level. Here we identify two receptor tyrosine kinase inhibitors (RTKIs) of the tyrphostin class that exhibit robust antiviral activity against influenza A virus replication in cultured cells. One of these (AG879) is a selective inhibitor of the nerve growth factor receptor and human epidermal growth factor receptor 2 (TrkA/HER2) signaling; the other, tyrphostin A9 (A9), inhibits the platelet-derived growth factor receptor (PDGFR) pathway. We find that each inhibits at least three postentry steps of the influenza virus life cycle: AG879 and A9 both strongly inhibit the synthesis of all three influenza virus RNA species, block Crm1-dependent nuclear export, and also prevent the release of viral particles through a pathway that is modulated by the lipid biosynthesis enzyme farnesyl diphosphate synthase (FPPS). Tests of short hairpin RNA (shRNA) knockdown and additional small-molecule inhibitors confirmed that interventions targeting TrkA can suppress influenza virus replication. Our study suggests that host cell receptor tyrosine kinase signaling is required for maximal influenza virus RNA synthesis, viral ribonucleoprotein (vRNP) nuclear export, and virus release and that specific RTKIs hold promise as novel anti-influenza virus therapeutics.