"It depends" Surprisingly it depends more on the opponent than the one throwing the punch.
Depending on circumstances, it could tear straight through (that is 100 tons of force!), or it might just push the opponent back. Certainly the opponent won't get the opportunity to say no.
By Newton's third law, if your hero can punch their opponent with 100kN of force, their opponent must be able to exert 100kN of force in the opposite direction. How they do that depends on their body. Take an example where they are up against a wall when this happens. They'll exert their 100kN of force by exerting 1000kN of force against the wall, holding them in place. In this case, the punch will have an effect worthy of any B-rate horror flick, because the only thing left to give is their body. Armor wont have any effect at all unless it is rated to withstand the combined weight of 2 M-1 Abrams tanks resting on it.
However, in the case where they can move, the story is a bit different. You can only exert 100kN of force if they can exert a corresponding amount of force back. If the punch is slow enough, you can punch with "up to" 1000kN of force, but you find yourself limited by the opponent moving backwards in response. Intuitively, if you were up against a hydraulic ram which was used to slowly bend steel tank armor, it would move slow enough that you'd get out of the way. The ram would never reach maximum force. To reach maximum force, you have to strike fast. That's where it starts getting interesting.
I say it gets interesting because the more agile your opponent is, the faster you're going to have to strike to achieve 1000kN. Striking a mosquito with 1000kN may require punch speeds far in excess of mach 1, because the mosquito has to be accelerated remarkably fast before F=ma can reach 1000kN. Fast accelerations are caused by high speeds with respect to the target's ability to respond.
If your punch ever exceeds the speed of sound in the opponent's fleshy chest, things start to get strange. You start to see shockwaves because the information about your punch cannot reach the opponent's extremities fast enough. This permits all sorts of strange sheering effects. I've heard NASA has some interesting videos of what hypersonic collisions look like.
If you're limiting yourself to human speeds for the punch, you wont be able to reach 1000kN without something like a brick wall behind your opponent. As a result, they will be exactly as unhappy as they set themselves up to be. A highly skilled martial artist may be able to react in a way to convert most of the energy into backwards motion for his entire body. A less skilled fighter may not, letting a massive amount of energy strike the front of his chest against the further back parts of his chest. His heart will not be happy.
Edit: given the clarifications we can explore more. If we assume the punch is fast enough that the recipient cannot get out of the way, the next layer of the question is pressure. How much pressure can you exert with your 1000kN of force, vs how much pressure can the object endure? The key for this is a concept known as "yield strength" this is a knee in the "stress-strain" curve. Below the yield strength, something will typically rebound back into its previous shape. Above that yield strength, it will permanently deform plastically.
You can do a lot of damage here with these forces. Take 4" rolled steel tank armor, used during WWII. It's yield strength is 688.5 MPa. Any pressure above that will permanently deform the steel in some way. If you have 1000kN at your disposal, you can deform the steel as long as you concentrate that force over 12 square centimeters (1000 kN / 950 MPa = 10.52 cm^2). The front surface of my fist is about 30 cm^2, so I couldn't quite damage the steel with the whole surface, but if I focused on my knuckles I could easily put a dent in 4" rolled steel. If I had sightly more force at my disposal, like 3000kN, I could actually put fist shaped indents in steel. If I could somehow sustain that 3000kN for the length of the entire punch, I could either severely dent that armor, or rip straight through, depending on the physics. The only real limit is the point where I move the tank rather than punch through it, which you explicitly took care of in your edit.
Now you can imagine the chunky salsa that will occur if we repeat that experiment with a human that doesn't get out of the way of this blow in time.