| The polepieces on your pickup aren't grounded.
I had that issue a while ago (about a year ago) and posted about it and how I solved it, with pictures... do a search on the archive.
Solutions:
1) The lazy way: get a new cover for your pickup that doesn't expose the polepieces.
2) Ground the polepieces. This is not always easy, it depends on how the pickup is constructed. If you can see the polepieces under the pickup, it can be as simple as laying a strip of adhesive copper shielding and grounding that. If it's a ceramic pickup... things may be more complicated.
3) Another lazy way: Nail varnish! No, seriously. It's easy, it's fast, and it works. And if you don't like it, easy to remove. Just remove the cover, paint the polepieces, and reassemble. You can buy black varnish, and disguise the polepieces that way. Or silver. Or colourless (my choice), or green for St. Patricks, or...
Get the stuff that dries fast, and apply 2-3 coats. It will wear out eventually, but it's easy to reapply. | 
Pick up buzzes when i touch it! 
