This paper reports a measurement by the T2K experiment of the νμ charged current quasielastic (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 ⟨σ⟩=(0.83±0.12)×10−38  cm2. The energy dependence of the CCQE cross section is also reported. The axial mass, MQEA, 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) pμ−cosθμ distribution, the effective MQEA parameter was measured to be 1.26+0.21−0.18  GeV/c2 (1.43+0.28−0.22  GeV/c2).