There appears to be some relationship between nations with higher minimum wage levels and nations with lower labor force participation.
Here is a graph comparing the level of the minimum wage and labor force participation in the US over time:
I don't want to make too much of this. There are so many factors that would influence LFP over time. For instance, the growth in LFP in the 1970's and 1980's was mostly attributable to cultural changes in female labor participation.
But, even in that case, the reduction in the real level of the minimum wage must have facilitated the entry of unskilled women into the labor force. Early minimum wage legislation had been applied only to women and children, sometimes with the aim of removing women from the labor force.
Considering the hand-wringing over voluntary decreases in labor force participation related to aging, proposals to raise the minimum wage back to around 50% of the average wage or more could reduce LFP by an additional 1% - 2%. Low labor force participation is a common problem for marginalized populations, so the disinterest in this concern among minimum wage proponents is odd.