A few things to consider....
It could be a near faulty switch in the fan that is arching when you turn it on and off. So, if you leave the switch in the "on" position and unplug the fan from the outlet, do you get the same result?
Next, I would check to make sure the outlet is wired correctly. I read somewhere about plugs being wired backwards and it created some type of noise issue (in amps, stereos, etc) when turning things on and off at that outlet.
What else is on that circuit? If you take the amp, run it through a LONG but adequate extension cord to another outlet on another circuit, then turn the fan on and off, do you get the same result?
Does this happen with other amps plugged into the same outlet?
If this is a new problem, something must have happened recently to cause this issue.