In an embodiment, a brown-out protection circuit includes: a monitoring terminal; a threshold generator supplying a threshold voltage; a comparator to compare a monitoring voltage at the monitoring terminal and the threshold voltage; and a logic module supplying an enable signal having a brown-in logic value and a brown-out logic value. When the enable signal is at the brown-out logic value, the logic module checks transition conditions, relating to a number of usable transitions of the monitoring voltage from lower to greater than the threshold voltage, and time conditions, relating to permanence of the monitoring voltage above the threshold voltage after a usable transition or in an aggregated manner after a plurality of consecutive usable transitions. The logic module sets the enable signal to the brown-in logic value when the transition conditions or the time conditions are met.