This is a common enough feat, see Avengers, Kung Fu Panda 2, RWBY, etc that it might be worth a calc.
So here we go.
My plan for this calc is to assume the average arrow catching feat involves the character starting with their hand and arm at resting position by their leg and catching the arrow at a distance equal to the length of the arrow away from their head.
I'll do a calc for a compound bow and one for a crossbow.
If I use that as the radius of the half circle created by swinging one's hand from their leg to their head, that gives the hypothetical circle a circumference of 4.59 meters
Half of which is 2.295 meters
(2.295*103.632)/0.76 = 312.941368421 m/s or Mach 0.91 or Transonic
(2.295*121.92)/0.508 = 550.8 m/s or Mach 1.6 or Supersonic
- Catching a Compound Bow Arrow: 312.941368421 m/s or Mach 0.91 or Transonic
- Catching a Crossbow Bolt: 550.8 m/s or Mach 1.6 or Supersonic