A current mirror circuit is provided with a first current mirror including first and second mirror transistors sharing a common control terminal; the first mirror transistor has a conduction terminal for receiving, during a first operating condition, a first reference current, and the second mirror transistor has a respective conduction terminal for providing, during the first operating condition, a mirrored current based on the first reference current. The current mirror circuit is provided with a switching stage operable to connect the control terminal to the conduction terminal of the first mirror transistor during the first operating condition, and to disconnect the control terminal from the same conduction terminal of the first mirror transistor, and either letting it substantially float or connecting it to a reference voltage, during a second operating condition, in particular a condition of stand-by.