Photonic radars are increasingly being developed and offer a promising replacement for traditional RF radars. They feature higher precision, and smaller size compared to the current microwave radars. One important part of a moving target indicating (MTI) radar is the Doppler shift measurement used to measure the radial velocity of a moving target. Therefore, for any photonic radar operating at MTI mode, it is necessary to have a Doppler measurement subsystem. In this paper, a microwave photonic Doppler frequency measurement system is conceived and implemented for this purpose specifically. The operation is based on making a Doppler shift-dependent yet low-frequency voltage component. It is all-optical and hence has the potential to be integrated into many electronic warfare systems. This feature not only makes the system independent of any sophisticated electrical device but also makes the measurement time lower than that of the electrical counterparts. The specific design presented here provides a much better stability compared to the recent works. An error as low as 0.012 Hz at a 10 GHz radar frequency was obtained, and the system performance was demonstrated up to 40 GHz, at which a 4.75 Hz error was recorded.