Eliminate all the variables that you can. Take out the audio cable from the back of the monitor and see if the buzz goes away. If it does, you may have a bad connection at one end of the cable (intermittent or shorted connections).
Are the monitors plugged into the same circuit? If so, then try to find out what else has been plugged into/added to that same CIRCUIT (not just the outlet) since you first noticed the buzzing. If they are not plugged into the same circuit, make it so and note any changes.
After you've done all that, it may be prudent to contact the manufacturer and see if it's covered under warranty.
If your monitor does this with NOTHING connected to the input, and with the volume control turned all the way down, then you likely have a blown power filter capacitor in the tweeter power amplifier. The only remedy is to send it in to be repaired. Hopefully it is still under warranty?
OTOH, if the noise (probably hum) goes away with the input disconnected, then your problem is upstream somewhere. You can swap left and right to do some differential diagnosis.