The D-League as petri dish for weird basketball concepts.
So I'm not a doctor, I'm just going off of personal experience and the picture that Kenny tweeted.
Based on the above picture (Thumb in a cast, other fingers free) and the fact that he'll be out 4-6 weeks I'm guessing Kenny has either a chip fracture at the base of his thumb or an Ulnar Collateral Ligament Tear. An x-ray would show which one it is. I have had 2 partial tears of my UCL and they hurt. (There is an Ulnar Cruciate Ligament, that's in the elbow and baseball players mess it up a lot). This injury is often referred to as skier's thumb because the method of injury happens a lot to skiers. It happens a lot to football players too. My first injury was when I tackled someone. Look at the back of your hand and pull your thumb down and towards you - that's the motion that the UCL prevents and how you can damage it. If Kenny slightly missed on a tackle - his thumb connecting with a shoulder or something but the rest of his hand didnt - and his thumb got bent back, that would lead to a UCL tear (my guess).
Depending on severity and if he needs surgery 4-6 weeks is a typical recovery. It's a joint that is easily taped and depending on his repair/recovery he should have no lasting effects. I had partial tears (no surgery or repair) and wasn't diagnosed for about 8 weeks after the first injury. My only medical restriction is that I'm not allowed to put my thumb in a bowling ball - all other sports and stuff are fine. Kenny's at Michigan, was diagnosed on sight and has some of the best medical care in the world. I'm sure he'll be fine come the fall. Here's wishing him the best during his recovery.