A novel Bayesian Hierarchical Network Model (BHNM) for ensemble forecasts of daily streamflow is presented that uses the spatial dependence induced by the river network topology and hydrometeorological variables from the upstream contributing area between station gauges. Model parameters are allowed to vary with time as functions of selected covariates for each day. Using the network structure to incorporate flow information from upstream gauges and precipitation from the immediate contributing area as covariates allows one to model the spatial correlation of flows simultaneously and parsimoniously. An application to daily monsoon period (July–August) streamflow at three gauges in the Narmada basin in central India for the period 1978–2014 is presented. The best set of covariates include daily streamflow from upstream gauges or from the gauge above the upstream gauges depending on travel times and daily precipitation from the area between two stations. The model validation indicates that the model is highly skillful relative to a null-model of generalized linear regression, which represents the analogous non-Bayesian forecast. The ensemble spread of BHNM accounts for the forecast uncertainty leading to reliable and skillful streamflow predictions.