Diagnosis
That's usually the fan motor itself getting noisy. Over time, the bearings can wear or dry out, or the fan blade can get slightly warped or unbalanced from heat, causing a loud humming or grinding vibration.
How to Fix It
First, rule out an obstruction. 1) Remove the grease filter(s) below the microwave. 2) Look up into the vent opening with a flashlight. Check for any debris—like a piece of packaging foam or a napkin—that might have fallen in during installation. Remove it if you can safely reach it. 3) Reinstall the filters. Often, just reseating the metal filters can change the resonance and quiet it down a bit.
If That Didn't Work
If the noise is clearly a mechanical grind from inside the unit, the fan motor assembly is likely the culprit. Replacing it involves taking the microwave down and opening the top casing, which is a significant repair. For a persistent, severe noise, a professional appliance tech is your best bet.
Heads Up
Don't ignore a fan that gets progressively louder and then stops working entirely. That motor also helps cool the magnetron (the part that makes the microwaves). Letting it fail can lead to a more expensive breakdown.