A microelectromechanical sensor device has a detection structure and an associated electronic circuitry, configured to receive, when the device is powered, an external power supply voltage and provided with a voltage regulator generating a regulated voltage and with at least one voltage domain powered by the regulated voltage. The electronic circuitry has a power supply management core, always powered by the external power supply voltage and which controls the voltage regulator to selectively interrupt the power supply of the voltage domain to implement: a first power-down condition wherein the voltage regulator is disabled; and a second power-down condition wherein the voltage regulator is enabled to power the aforementioned voltage domain through the regulated voltage, the first and the second power-down conditions being associated with absence of data acquisition and/or processing by the sensor device. The power supply management core automatically enables the first or second power-down condition upon a first power-on of the sensor device, as a function of a configuration signal, programmable, for example, during a factory calibration step.