Dynamic scaling in braided rivers is reexamined under an extended theoretical framework, developed herein, which explicitly incorporates the self-affinity (scaling anisotropy) in the spatial structure of braided rivers. It is shown that in structures exhibiting anisotropic spatial scaling, dynamic scaling (if present) is necessarily anisotropic. Through analysis of the behavior of an experimental braided river, the presence of anisotropic dynamic scaling in braided rivers was revealed. This implies that there exists a pair of dynamic exponents z(x) and z(y) enabling one to rescale space (differently in the direction X of the slope and m the perpendicular direction Y) and time, such that the evolution of a smaller part of a braided river looks statistically identical to that of a larger one. The presence of such a space-time scale invariance provides an integrated framework for describing simultaneously the spatial and temporal structure of braided rivers and may be explored toward statistical prediction of large and rare changes from the statistics of smaller and frequent ones.