Min wage should not exist in a free market, by definition. A society where it does exist is not a free market.
Regardless, the practical benefit of such laws (assuming they're rigidly enforced, which they're not) is the upgrading of wages in a monopsonistic labor market.
From a libertarian perspective, the relevant question to ask is why does a labor market become a monopsony. Typically, that happens solely because of
1) Bureaucratic restrictions/regulations (license fees, insurance requirements, taxes, etc.) on the entry of businesses into the market. In many cases, those regulations have nothing to do w/the legal liabilities that business may incur, but are simply imposed by a state or other government entity.
2) Inability to access credit due to legal restrictions (i. e. unrelated to creditworthiness of the applicant).
In a pure free market (where the capital resources were distributed prior to the initiation of that market), neither of the above 2 conditions exist, so monopsonies and monopolies are unlikely to form, so min wage wouldn't be needed in such a system.