Need to filter low voltage from a piezo buzzer circuit
Not every buzzer is a piezo buzzer and not every buzzer does the buzzing by itself. Some buzzers have only a piezo disc and for those a tone signal is needed to make it beep. Other buzzers only need a DC voltage and they start buzzing at a fixed frequency. The actual sound can be generated with a piezo or a electro-magnetic element (like a mini speaker).

I'm not sure which buzzer you have. I think it will not draw a lot of current, therefor a zener diode of 5.6V should work.