A MEMS sensor has at least a movable element designed to oscillate at an oscillation frequency, and an integrated measuring system coupled to the movable element to provide a measure of the oscillation frequency. The measuring system has a light source to emit a light beam towards the movable element and a light detector to receive the light beam reflected back from the movable element, including a semiconductor photodiode array. In particular, the light detector is an integrated photomultiplier having an array of single photon avalanche diodes.