Magnetic ordering in the geometrically frustrated magnetic oxide spinels MgCr2O4 and ZnCr2O4 is accompanied by a structural change that helps to relieve the frustration. Analysis of high-resolution synchrotron x-ray scattering reveals that the low-temperature structures are well described by a two-phase model of tetragonal I41/amd and orthorhombic Fddd symmetries. The Cr4 tetrahedra of the pyrochlore lattice are distorted at these low-temperatures, with the Fddd phase displaying larger distortions than the I41/amd phase. The spin-Jahn-Teller distortion is approximately one order of magnitude smaller than is observed in first-order Jahn-Teller spinels such as NiCr2O4 and CuCr2O4. In analogy with NiCr2O4 and CuCr2O4, we further suggest that the precise nature of magnetic ordering can itself provide a second driving force for structural change.