An offset-compensation circuit in a MEMS sensor device, provided with a micromechanical detection structure that transduces a quantity to be detected into an electrical detection quantity, and with an electronic reading circuit, coupled to the micromechanical detection structure for processing the electrical detection quantity and supplying an output signal, which is a function of the quantity to be detected. A compensation structure is electrically coupled to the input of the electronic reading circuit and can be controlled for generating an electrical compensation quantity, of a trimmable value, for compensating an offset on the output signal; the compensation circuit has a control unit, which reads the output signal during operation of the MEMS sensor device; obtains information on the offset present on the output signal itself; and controls the compensation structure as a function of the offset information.