Have you had a problem with ear ringing and ibuprofen before? It doesn’t hit everyone like that, so if you don’t have a history of it, I wouldn’t worry about it.
But if you do have experience with it and it’s a problem for you, then…yeah, that’s a problem. It’s usually dose dependent, meaning that there may be a smaller dose that will give you the effect the dentist is looking for but will not cause the ringing in your ears. So if he’s suggesting, say, 600mg every 4 hours, ask him if you can try 400 instead. That may still be enough to reduce the inflammation, and if you’re lucky, not cause the ringing.
If he’s suggesting it to control pain, as well, ask him what he thinks of adding an extra strength Tylenol to the regimen. Ibuprofen and Tylenol work to prevent pain in slightly different ways, and particularly with dental pain, many patients find more relief using the two together than either one alone.
The annoying thing is that Tylenol should be taken every 6 hours, and Ibuprofen every 4 hours. They will coincide twice a day, but other than that, you can’t take them at the same time on the clock. It’s not safe to take Tylenol more often, and it won’t control most people’s pain well enough to take the ibuprofen less often. It’s a dilemma. I suggest just setting a couple of timers in your cell phone to go off every 4 and 6 hours and label them “Ibuprofen” and “Tylenol” respectively so you’ll know what to take when. Otherwise you’ll probably lose track. I know I do, if I try to wing it, and I give out medicine for a living! 
If you can’t find a dose of ibuprofen low enough to control the inflammation and not cause ringing, then he needs to decide how medically necessary reducing that inflammation is. If it’s a pain thing, there are other pain medications he can prescribe, like Norco or Vicodin. If it’s truly an inflammation thing, he may need to consider a short course of steroids instead of NSAIDS. All NSAIDS, as far as I can tell from my drug books, are culprits for ear ringing, internal ear damage and hearing loss in susceptible people.