Novel antiviral agents for influenza, which poses a substantial threat to humans, are required. Cyclobakuchiols A and B have been isolated from Psoralea glandulosa, and cyclobakuchiol C has been isolated from P. corylifolia. The structural differences between cyclobakuchiol A and C arise due to the oxidation state of isopropyl group, and these compounds can be derived from (+)-(S)-bakuchiol, a phenolic isoprenoid compound present in P. corylifolia seeds. We previously reported that bakuchiol induces enantiospecific anti-influenza A virus activity involving nuclear factor erythroid 2-related factor 2 (Nrf2) activation. However, it remains unclear whether cyclobakuchiols A–C induce anti-influenza A virus activity. In this study, cyclobakuchiols A, B, and C along with cyclobakuchiol D, a new artificial compound derived from cyclobakuchiol B, were synthesized and examined for their anti-influenza A virus activities using Madin-Darby canine kidney cells. As a result, cyclobakuchiols A–D were found to inhibit influenza A viral infection, growth, and the reduction of expression of viral mRNAs and proteins in influenza A virus-infected cells. Additionally, these compounds markedly reduced the mRNA expression of the host cell influenza A virus-induced immune response genes, interferon-β and myxovirus-resistant protein 1. In addition, cyclobakuchiols A–D upregulated the mRNA levels of NAD(P)H quinone oxidoreductase 1, an Nrf2-induced gene, in influenza A virus-infected cells. Notably, cyclobakuchiols A, B, and C, but not D, induced the Nrf2 activation pathway. These findings demonstrate that cyclobakuchiols have anti-influenza viral activity involving host cell oxidative stress response. In addition, our results suggest that the suitably spatial configuration between oxidized isopropyl group and phenol moiety in the structure of cyclobakuchiols is required for their effect.