T2K has performed the first measurement of νμ inclusive charged current interactions on carbon at neutrino energies of ∼1  GeV where the measurement is reported as a flux-averaged double differential cross section in muon momentum and angle. The flux is predicted by the beam Monte Carlo and external data, including the results from the NA61/SHINE experiment. The data used for this measurement were taken in 2010 and 2011, with a total of 10.8×1019 protons-on-target. The analysis is performed on 4485 inclusive charged current interaction candidates selected in the most upstream fine-grained scintillator detector of the near detector. The flux-averaged total cross section is ⟨σCC⟩ϕ=(6.91±0.13(stat)±0.84(syst))×10−39  cm2nucleon for a mean neutrino energy of 0.85 GeV.