I get this, mostly on the more bumpy runs, although I do ride a hardtail. I've not yet figured out the cause but have come up with some ideas:
Over-gripping the bars (ie holding on too tightly)I've tried experimenting with holding on to the bars less tightly, but this seems to make it worse as you seemingly get more vibration.
Grips too small/largeI havn't tried any different grips yet
Brake lever reach too far awayThought maybe that over reaching would do something to the joints. As you were getting the same problem even without one of the brakes maybe this is discounted.
Brake lever angle wrongly setMy levers are pretty much in line with my arms and it seems comfortable at other times.
Arthritis or some kind of "white finger"?