This is a major update to everyone who has responded to my thread.
I went to the Apple Store today and it was unfortunately, an incredibly frustrating and disappointing experience for me. I talked to the Support Supervisor and he was very unhelpful:
He told me that this issue is "really a small issue" because it's the first time "he's" heard of it so he says it's not really a big enough issue for Apple to pay attention to right now.
Basically, what you said J.Tauber, is probably correct. A software change must have trigger some sort of a hardware change. This vibrate dysfunction happened right after I updated. I didn't drop my phone in water or anything.
However, Apple tells me that there's nothing they can do, because after restoring the phone to factory settings, the vibrate still doesn't work and this is "their proof" that the problem is not a software related issue. I was under my 1-year Apple warranty when the issue happened (the day I upgraded to iOS7). I even posted this thread a week before my 1-year Apple warranty ended. However, I was out of the country until a week ago, and even though I took this to the Apple Store as soon as I got back, they are telling me that there is nothing they can do because I am "30 days" outside of the Apple Warranty.
This is incredibly disappointing that Apple doesn't really care "what goes on" in these Apple Support Communities. They don't care that I brought this issue up (while I was in India) before my 1-year warranty was over. They don't care that this happened to me right after the iOS7 update (along with many of others who posted in this thread)
My recommendation for everyone is to call their PHONE number support service and open up a case with Apple has it "officially" on file, especially before your 1-year warranty or Apple Care expires.
If you don't have Apple Care and you're outside your 1-year warranty YOU'RE OUT OF LUCK. Apple does not care about your phone at this point neither will they really work hard to satisfy you as a customer. You'll probably have to take it to the Apple store and pay whatever the service fee is to change out the Vibrate Motor and there's no guarantee it'll work then.
I'm having the vibrate motor replaced right now and we'll see if it does anything. I think I'm done with Apple products after this. I got to see first hand how they are LESS about helping customers and more about selling their Apple Care warranties: if you're a day outside of it and the issue was caused by their software update, they still think that it's not their problem.
I got my iPhone back today after paying a $35 service fee, the vibration works again but if it had not been fixed, they said the only other option (outside of Apple Care) woud've been to have purchase another phone.