Matrix proteins from enveloped viruses play an important role in budding and stabilizing virus particles. In order to assess the role of the matrix protein M1 from influenza C virus (M1-C) in plasma membrane deformation, we have combined structural and in vitro reconstitution experiments with model membranes. We present the crystal structure of the N-terminal domain of M1-C and show by Small Angle X-Ray Scattering analysis that full-length M1-C folds into an elongated structure that associates laterally into ring-like or filamentous polymers. Using negatively charged giant unilamellar vesicles (GUVs), we demonstrate that M1-C full-length binds to and induces inward budding of membrane tubules with diameters that resemble the diameter of viruses. Membrane tubule formation requires the C-terminal domain of M1-C, corroborating its essential role for M1-C polymerization. Our results indicate that M1-C assembly on membranes constitutes the driving force for budding and suggest that M1-C plays a key role in facilitating viral egress.