It's not the only way though. We have no legally defined or mandated minimum wage here in Norway (nor elsewhere in the Nordic region I think). But the effective minimum is probably higher than the mandated minimum in any other country.
Broadly speaking the way it is done here is that the national association of employers and the principal unions negotiate a tariff for each industry and type of work each year. The state is involved to the extent that it provides an official who acts as referee in the negotiations and tries to chivvy the parties to an agreement.
Employers are free to ignore the rules but risk losing employees to companies that pay according to the tariff.
Of course the difference between here and the US is that solidarity is stronger here so the negotiations are less hostile here.
It's not perfect but it seems to work quite well
I'm very capitalistic and libertarian, but reality is all systems need to manage edge cases. Minimum wage is a part of that. To believe that the market can figure everything out requires serious tunnel vision.