(Looks like this has been discussed above, my bad)
I've seen this a couple of times, but from what I've read below, it was on his throwing hand:
"It's A New Me": Joe Milton Is Healthy And Ready To Battle For QB1 At Tennessee | Rocky Top Insider
(This article says it explicitly)
‘It’s a new me’ — Joe Milton III joining Vols with renewed confidence
(This article discusses how he "resumed throwing" at a time following surgery, the implication being that the surgery prevented him from throwing for some time.)
Michigan QB Joe Milton sports cast in social media video
(This article demonstrates that his right hand - his throwing hand - was what was injured)
PressReader.com - Digital Newspaper & Magazine Subscriptions
(This article discusses his right hand being in a cast post surgery)
I believe the misconception comes from the fact that the Instagram video (and the screen shots from that) are mirrored in a way that makes it appear that his left hand is the one that is in the cast.