The group said many poorly-paid workers had been forced to rely on foodbanks and charities.
One Fair Wage has already received support from the Scottish Government, the Scottish Labour Party, Unison and Save the Children.
Angela Constance, minister for youth employment, said: "Living wage is an important part of a package of Scottish Government policies to support sustainable employment and tackle poverty.
"We have demonstrated our full support for the campaign's principles by implementing the living wage through Scottish public-sector pay."
Kez Dugdale, Labour's shadow youth employment minister, said: "Two-thirds of the children living in poverty come from working households. Work simply has to pay if we want to live in a more equal and fair society, and I look forward to working very closely with SYP to turn that dream into a reality."