I know my grandma's house (which was built c. 2005) has a 20 amp AFCI breaker for the bedroom circuit that buzzes. Never noticed it until I was in the basement once and heard a faint buzzing coming from the breaker panel. I don't think this is really a cause for concern though because AFCI and GFCI breakers have integrated electronics that detect when a fault has occurred to trip the breaker. The GFCI outlet that I replaced in my bathroom about 10 years ago also emits a faint buzz but you cannot hear it unless you get really close to it, and it works just fine. Occasionally I test it just to make sure it still trips and it does.

I would also check for doorbell transformers which are often mounted directly onto the panel or near it (such as on an outlet box next to the panel), or even in the form of a "wall wart" plugged into a nearby outlet. I've encountered loud doorbell transformers that fill the room with their harmonic buzz. This is especially common as the transformers age, they aren't like the pole transformers outside your house that seem to last forever. A loud doorbell transformer should still work and isn't a hazard but can be a nuisance. Luckily replacement transformers are pretty cheap and can be picked up at any home improvement center or even a local hardware store. Walmart probably sells them too.

If you can't rule out the cause of the buzzing then you should definitely call an electrician because there might just be a loose connection arcing inside the panel. When large currents are drawn the connection is going to heat up and the arcing will worsen, and you risk burning your house down.