While that may still be the case today, the origins of the minimum wage laws actually have a darker history. The harm to the poor was not incidental; it was its declared purpose.
Part of a package of “progressive” eugenics policies just over 100 years ago, alongside abortion and forced sterilization, proponents of minimum wage laws like Henry Rogers Seager, a Columbia economist and president of the American Association for Labor Legislation, published a key paper on minimum wage laws in 1913, “If we are to maintain a race that is to be made up of capable, efficient and independent individuals and family groups we must courageously cut off lines of heredity that have been proved to be undesirable by isolation or sterilization of the congenitally defective."
Reading the published policy proposals by the “progressive" Democrat leaders of the time is chilling. I recommend James Corbett's short documentary, "The Dark History of the Minimum Wage."