I can appreciate the desire to ensure criminals have some money when they get out since a lot of crime is correlated with poverty and job prospects are slim. However, you're neglecting that prosecuting and incarcerating people costs society money, which is to say that criminals owe society a debt, and in principle, criminals should be paying as much of that debt as is feasible.

That said there are multiple ways to do this. One is compelled labour the proceeds of which they'll never see, but perhaps work can go to lowering their sentence. Another can be deferred compensation, where they get a fixed stipend once out based on their work while incarcerated.

I can think of a bunch of other ways, but I'm not sure I agree that the compensation should be minimum wage. People fund the government via taxes, but criminals aren't just not paying into the system, they are actively draining it. I'm not sure garnishing wages they'd otherwise earn is in principle unjust anymore that income tax is unjust.