The weak nucleon axial-vector form factor for quasielastic interactions is determined using neutrino interaction data from the K2K Scintillating Fiber detector in the neutrino beam at KEK. More than 12000 events are analyzed, of which half are charged-current quasielastic interactions νμn→μ-p occurring primarily in oxygen nuclei. We use a relativistic Fermi gas model for oxygen and assume the form factor is approximately a dipole with one parameter, the axial-vector mass MA, and fit to the shape of the distribution of the square of the momentum transfer from the nucleon to the nucleus. Our best fit result for MA=1.20±0.12GeV. Furthermore, this analysis includes updated vector form factors from recent electron scattering experiments and a discussion of the effects of the nucleon momentum on the shape of the fitted distributions.