The families of former miners have been asked to contribute to a sculpture which sits at the centre of the garden.
Lives Lived Lives Lost is a steel structure which has space to hold glass discs containing miners' names.
The Matlby Miners Welfare Band performed at the opening ceremony, which also included short readings.
Rosemary Priest, from the museum, said the idea for the garden had come from visitors: "They wanted somewhere they could sit and think about the people who had lived or died within the industry."
She said the sculpture, commissioned from artist Stephen Broadbent, stood about 9ft (3m) high and curved round in a sweeping arc.
It is designed to suggest a seam of coal pierced by mine workings. The glass discs are placed into channels representing the shafts and levels of a mine.
Only a few discs have been placed into the sculpture so far, enabling visitors to continue contributing the names and dates of relatives from the industry.
The museum said it would be adding discs to the sculpture several times a year.
A garden dedicated to those who worked in the mining industry has been opened at the National Coal Mining Museum near Wakefield.