Sounds like some sort of resonance thing, for sure. Like someone else suggested, try it with another guitar; that will narrow the source of the noise down to the guitar or amp. If it's a tube amp and it does this with different guitars but on the same note, then with the amp powered up, gently tap on each tube with a pencil and see if one tube in particular gives you the same noise. If it's a preamp tube, then simply replace it. If it's a power tube, then you may want to consult an amp tech; there's tube matching and bias to consider.
If it's the amp, but not a tube, then you'll have to get into the amp to take a look, but if you're not experienced at dealing with the inner workings of amps, then take it to a tech. There are voltages in there that can kill you even with the amp powered down and disconnected.
Buit you've been around here a while and read all that before, eh?