We present the first measurement of the atomic mass dependence of central \Xi~- and \overline{\Xi}~+ production. It is measured using a sample of 22,459 \Xi~-'s and \overline{\Xi}~+'s produced in collisions between a 250 GeV \pi~- beam and targets of beryllium, aluminum, copper, and tungsten. The relative cross sections are fit to the two parameter function \sigma_0 A~\alpha, where A is the atomic mass. We measure \alpha = 0.924+-0.020+-0.025, for Feynman-x in the range -0.09 < x_F < 0.15.