Just had the same problem, My sony Z is a repaired one just over a month old. It is Always in a Leather Case. Just 15 min ago the Phone just started vibrating (thought it was a call) non stop. Turned the Phone off but didn't stop. Turned it on again but nothing changed.
meanwhile searched the web for solutions, only thing i could find that it was hardware related.
Since the Phone is little to big for my pocket i thought it could be from flexing the Phone or something like that. So i put it back in it's case, and put it flat on my hand and gave it a firm tap on the back with my other hand. The 2nd try was succesfull and the Phone stopped vibrating.
Checked if normal vibration still works and found no problems.
My experience with the latest Phones is getting worse with every model they (HTC / Sony) release. Feels like the phones suffer more and more from stupid (hardware) problems. Looks like the Urge of releasing a new model every half year is showing its flaws...