This is a pretty good match-up (better than Oonoki vs. Minato lol). Alright, here's my two cents on this. Now Minato clearly has the advantage in movement speed. However, Muu has shown that he is not only a highly proficient sensor ninja, but has fantastic reflexes (being that he easily dodged Naruto he tried to sneak up on him from behind).
As I have said many, many times there are different types of "speed". Minato's reflexes and movement speed are probably beyond Muu's (especially movement speed). However, merely because one's movement speed is superior than another's, this does not mean the ninja with the slower movement speed will necessarily be blitzed. We plainly see a clear example of this, with Sasuke reacting to everything that A was doing, even with his V2 Shroud. Sasuke dodged A's Elbow head-on, he activated Susanoo to shield himself from A's Raiger Bomb, shrouded his Susanoo with Amaterasu to counter A's Raigyaku Shuhei (after he just dodged Amaterasu), he activated Enton: Kagutsuchi to counter A's Guillotine Drop. Believe it or not, Sasuke was able to effectivelyreact to everything A did, even though A is vastly superior in movement speed.
With that said, I believe that Muu should atleast be able to react to Minato's basic Shunshin no Jutsu.
As far as sensing Muu goes, this all depends on whether or not Muu is on the ground or flying when the battle first begins. If he's on the ground, Minato's finger trick will certainly locate him. But if he's flying,Minato hasno means of locating Muu. Despite this, even if Muu is flying through the air while invisible, Minato will still be able to see Muu's actual technique both during it's charging stage and it's firing stage. Muu is invisible, but I don't think his Jinton is though. Although Minato is not the type to immediately blitz people off the bat, if Minato is fully aware of Muu's abilities, then I can see Minato trying to blitz Muu immediately just to "mark" him. If he's marked, then Minato should be able to now counter his invisibility, by simply using Hiraishin to teleport to his location.
Space-Time Barrier Jutsu should be more than enough to counter any Jinton technique. If they are able to easily consume Full Power Kyuubi's TailedBeast Bomb, then I can't see Muu producing a large or strong enough attack that Minato wouldn't be able to stop or redirect.
The problem for Minato, is that once Muu decides to start flying, Minato will have a problem getting to him.If he doesn't manage to mark Muu before he takes flight, the only way Minato would be able to potentially reach him, is if he has Gamabunta or one of his Giant Toads jump around after him. But even then, that's going to be very difficult. Especially since Muu will be constantly be attacking with Jinton, and Minato will have to constantly protect himself and his Toads with his S/T Barriers.
Minato can't seal Muu. Atleast not without using Shiki Fujin, which would kill himself aswell. I wouldn't be surprised if Minato does have sealing jutsu that can bind an Edo Tensei (since he is skillful in sealing, and Kushina is master in the art and taught him such jutsu). However, because we haven't seen any such Fuinjutsu from Minato, it's not fair to simply assume that he can. The only thing I can see Minato doing, is weakening Muu with a well placed Rasengan (his normal Rasengan are at least as strong as Naruto's Oodama Rasengan) then having Gamabunta sit on Muu or something, which would effectively pin him down lol.
I can see Minato winning high difficulty tho.
