When wage setting is more regulated, the gender wage gap tends to decrease. We examine whether this holds for a complex system of occupation- and industry-specific minimum wages, which cover both low-pay and high-pay segments of the labour market. The system has the potential to close the gender wage gap by ensuring equal minimum pay for equal jobs, but it also has the potential to widen it by discriminating against jobs more commonly held by women. We carefully describe wage levels as well as returns to experience and their association with individual gender as well as the male employment share in the individual's field (industry or occupation) of work. We find that the gender wage gap among employees receiving a minimum wage is less than half the magnitude of the gap among other employees. Despite this, there is nonetheless evidence that, within the minimum-wage system, there is a wage penalty for employment in jobs more commonly held by women, although only for employees without university degrees. Our results suggest that, for university-educated women, the regulated setting of minimum wages helps to close the gender wage gap and counteracts the undervaluation of work typically undertaken by women. However, for less-educated women, who comprise approximately 82% of female minimum-wage employees, minimum wages could do more to close the gender wage gap if they were neutral with respect to the gender composition of jobs.