Yes he would be injured. Think of it this way ...his clone is hitting him with fists pf the exact same durability as his body.
Or maybe think of it another way. You have one M1A2 Abrams tank, and a second one is lifted up on a strong crane and dropped on the first one. There's a good chance it will be dented. The Abrams' Chobham armor is very strong, but it is being hit by another Abrams tank with exactly the same armour strength. That would be a very different effect from, say, hitting the same tank with a Toyota!
Or maybe think of it in this way. Imagine you stand in front of a mirror and you decide to punch yourself in the face. Hard. Will you get injured?
Superman could injure himself since he would be hitting himself with ...well, himself.
The long answer you received a minute ago is largely correct, at least as regards any modern Superman. If you came up with this question because you happened upon one of his ridiculous 1960s adventures, however, then the answer would be "Yes, Superman's durability would protect him, and any other Earthbound Kyptonian, from even Superman 's hardest punches". 1960s "Super"-type invulnerability trumped almost anything this side of Fawcett Comics, outstripping even the vast levels of physical strength that Superman, Superboy, and Supergirl were known for.