This paper reports the first differential measurement of the charged-current $\overline{\nu}_{\mu}$ interaction cross section on water with no pions in the final state. The unfolded flux-averaged measurement using the T2K off-axis near detector is given in double differential bins of $\mu^+$ momentum and angle. The integrated cross section in a restricted phase space is $\sigma=\left(1.11\pm0.18\right)\times10^{-38}$ cm$^{2}$ per water molecule. Comparisons with several nuclear models are also presented.