An enzyme that catalyzes the hydrolysis of cerebroside 3-sulfate (sulfatide) to yield a cerebroside and inorganic sulfate. A marked deficiency of arylsulfatase A, which is considered the heat-labile component of cerebroside sulfatase, has been demonstrated in all forms of metachromatic leukodystrophy (leukodystrophy, metachromatic). EC 3.1.6.8.