It depends on what is causing the buzz. Can you see it touching the frets anywhere? If not, this might not be your problem.

What can happen (if you're very unlucky) is that the tension and length of the bit of string from the nut to the tuner resonates. If you're fretting the string then your finger deadens the string above that point, but on an open string the nut is taking the strain and a certain amount of the vibration will get through. Try putting a bit of tape around that bit of the string, and that'll stop any resonance dead. I've just had myself a similar symptom on my classical (coincidentally also on the A string), and I've also had the same happen with my violin E-string between the bridge and tailpiece.

I can't guarantee it, but if it doesn't work then you've lost nothing except a 1" piece of Sellotape. :-)

Graham.