The Charged-Current Quasi-Elastic (CCQE) interaction, νl+n→l−+p, is the dominant CC process at Eν∼1 GeV and contributes to the signal in accelerator-based long-baseline neutrino oscillation experiments operating at intermediate neutrino energies. This paper reports a measurement by the T2K experiment of the νμ CCQE cross section on a carbon target with the off-axis detector based on the observed distribution of muon momentum (pμ) and angle with respect to the incident neutrino beam (θμ). The flux-integrated CCQE cross section was measured to be (0.83±0.12)×10−38 cm2 in good agreement with NEUT MC value of 0.88×10−38 cm2. The energy dependence of the CCQE cross section is also reported. The axial mass, MAQE, of the dipole axial form factor was extracted assuming the Smith-Moniz CCQE model with a relativistic Fermi gas nuclear model. Using the absolute (shape-only) pμcosθμ distribution, the effective MAQE parameter was measured to be 1.26+0.21−0.18 GeV/c2 (1.43+0.28−0.22 GeV/c2).