This paper proposes a fuzzy entropy-based methodology for optimal design and performance assessment of a hydrometric monitoring network that provides information essential for hydrological studies. The methodology does not require choice of bin size for discretization of data to estimate entropy measures/indices. Therefore, it alleviates the uncertainty associated with bin size estimation which is a concern in analysis with conventional Shannon entropy-based methodology (SEBM). Advantage of the proposed methodology over SEBM and its related theoretical improvement EEBM (exponential entropy-based methodology) in arriving at optimal design of streamflow monitoring network is demonstrated through performance investigation on Mahanadi basin of India, which is frequently prone to floods. Following this, the methodology is used to assess the performance of streamflow monitoring networks in 16 river basins of Peninsular India and identify stream gauge deficit zones. This study is first of its kind which evaluates the effect of different entropy estimation methods and bin size estimation rules on: (i) prioritization of stream gauge stations for their importance in data collection, (ii) identification of stream gauge deficit zones, and (iii) design of optimal hydrometric network in a river basin. Proposed methodology appears promising and offers scope for application to networks monitoring various other hydrometeorological variables.