A MEMS accelerometer, including: a support structure (3); a suspended region (2; 62; 92) made of semiconductor material, mobile with respect to the support structure; at least one modulation electrode (20; 68; 114), which is fixed to the support structure and is biased with an electrical modulation signal including at least one periodic component having a first frequency; at least one variable capacitor (30; 80; 130), formed by the suspended region and by the modulation electrode, in such a way that the suspended region is subjected to an electrostatic force that depends upon the electrical modulation signal; and a sensing assembly (12, 14, 16, 18, 5a; 12, 14, 16, 18, 65a; 102, 104, 95a), which generates, when the accelerometer is subjected to an acceleration, an electrical sensing signal, which indicates the position of the suspended region with respect to the support structure and includes a frequency-modulated component, which is a function of the acceleration and of the first frequency.