I'm going to disagree with the second part of your comment, because it implies that the employee being hired wouldn't be willing to do it for less themselves.
In any case, without a minimum wage, low-skill wages become a race to the bottom as people become more and more desperate for work. Someone might be willing to work for $1/hour because they're fine living in a cardboard box behind their workplace and eating scraps from the garbage.
But that only allows income inequality to worsen. The rich get even richer as they sit back and laugh as the employees essentially auction themselves to lower and lower wages. Upward mobility dies as the ability to seek extra education and training disappears because you gotta work 100 hours/week just to survive.
So yeah, I suppose minimum wage breaks supply and demand for wages, but I'd argue that's a damn good thing.