The minimum wage was established - along with a variety of other rules related to labor - in the
Fair Labor Standards Act, a piece of New Deal legislation passed in 1938.
The proposal . . . adopted an eight-hour day and a forty-hour workweek and allowed workers to earn wage for an extra four hours of overtime as well. According to the act, workers must be paid minimum wage and overtime pay must be one-and-a-half times regular pay. Children under eighteen cannot do certain dangerous jobs, and children under the age of sixteen cannot work during school hours.
If I'm not mistaken, the bill was responsible for creating what we now know as a weekend.