The measurement of extremely small displacements is of utmost importance for fundamental studies and practical applications. One way to estimate a small displacement is to measure the Doppler shift generated in light reflected off a moving object, converting a displacement measurement into a frequency measurement. Here we show a sensitive device capable of measuring μHz/Hz Doppler frequency shifts corresponding to tens of femtometer displacements for a mirror oscillating at 2 Hz. While the Doppler shift measured is comparable to other techniques, the position sensitivity is orders of magnitude better, and operates over several orders of magnitude of Doppler frequency range. In addition, unlike other interferometric techniques, our device is phase insensitive, making it unusually robust to noise.