Influenza A virus is a serious human pathogen that assembles enveloped virions on the plasma membrane of the host cell. The pleiomorphic morphology of influenza A virus, represented by spherical, elongated, or filamentous particles, is important for the spread of the virus in nature. Using fixative protocols for sample preparation and negative staining electron microscopy, we found that the recombinant A/WSN/33 (H1N1) (rWSN) virus, a strain considered to be strictly spherical, may produce filamentous particles when amplified in the allantoic cavity of chicken embryos. In contrast, the laboratory WSN strain and the rWSN virus amplified in Madin–Darby canine kidney cells exhibited a spherical morphology. Next-generation sequencing (NGS) suggested a rare Ser126Cys substitution in the M1 protein of rWSN, which was confirmed by the mass spectrometric analysis. No structurally relevant substitutions were found by NGS in other proteins of rWSN. Bioinformatics algorithms predicted a neutral structural effect of the Ser126Cys mutation. The mrWSN_M1_126S virus generated after the introduction of the reverse Cys126Ser substitution exhibited a similar host-dependent partially filamentous phenotype. We hypothesize that a shortage of some as-yet-undefined cellular components involved in virion budding and membrane scission may result in the appearance of filamentous particles in the case of usually “nonfilamentous” virus strains.