River discharge is an important variable to measure in order to predict droughts and flood occurrences. Once the cross-section geometry of the river is known, discharge can be inferred from water level and surface flow velocity measurements. Since river discharges are of particular interest during extreme weather events, when river sites cannot be safely accessed, noncontact sensing technologies are particularly appealing. To this purpose, the present work proposes a prototype of a low-cost Continuous Wave (CW) Doppler radar sensor, able to monitor the surface flow velocity of rivers. The prototype is tested at two gauged sites in central Italy, along the Tiber River. The surface flow velocity distribution across the river is monitored by means of the analysis of the received Doppler signal. The surface velocity statistics are then extracted using a novel algorithm that is optimized to run on a microprocessor platform with minimal computing power (ArduinoUNO). In particular, the radar measurements are used to initialize a 2D Entropy-based Velocity Model (EVM) that is able to estimate river discharges in any flow condition. Finally, the results concerning the observed discharge provided by the EVM prove to be comparable with those obtained with more expensive commercial solutions. The results are important since the described methodology can be extended to small-size Doppler radar sensors onboard Unmanned Aerial Vehicles (UAVs), the latter providing a method for mapping surface velocity of rivers.