My first initial thoughts -
Potential ground loop. Guitar amps are notorious for this.
Preamp or mic may have a lot of self noise. Perhaps this pre or mic is inexpensive? Even several of the expensive stuff can be noisy.
Not all mics output the same strength output... For example, ribbon mics really need a strong preamp. Depending on mic's output, you could be potentially turning the gain of the preamp much higher than you would need to for a different microphone model.
Could be your monitoring system, and not the mic or pre. Without the mic and pre powered on, when you bring up the levels to where to like them, that could be the problem child.
Or maybe its the room - A/C, bleed from a computer fan,...
Tainted electricity - an outlet on the A/C or refigerator circuit.
...Unbalanced signal chain, as mshilarious stated.
Tinnitus is always probable cause.
(More adjectives and nouns would've been helpful - equipment used, description of the buzz...)
