The integration of Microbial Fuel Cells (MFCs) in a microfluidic geometry can significantly enhance the power density of these cells, which would have more active bacteria per unit volume. Moreover, microfluidic MFCs can be operated in a continuous mode as opposed to the traditional batch-fed mode. Here we investigate the effect of fluid flow on the performance of microfluidic MFCs. The growth and the structure of the bacterial biofilm depend to a large extent on the shear stress of the flow. We report the existence of a range of flow rates for which MFCs can achieve maximum voltage output. When operated under these optimal conditions, the power density of our microfluidic MFC is about 15 times that of a similar-size batch MFC. Furthermore, this optimum suggests a correlation between the behaviour of bacteria and fluid flow.