This paper reports the first differential measurement of the charged-current interaction cross section of νμ on water with no pions in the final state. This flux-averaged measurement has been made using the T2K experiment's off-axis near detector, and is reported in doubly differential bins of muon momentum and angle. The flux-averaged total cross section in a restricted region of phase space was found to be σ=(0.95±0.08(stat)±0.06(det syst)±0.04(model syst)±0.08(flux))×10−38cm2/n.