By studying the dielectric properties of the geometrically frustrated spinel CdV2O4, we observe ferroelectricity developing at the transition into the collinear antiferromagnetic ground state. In this multiferroic spinel, ferroelectricity is driven by local exchange striction and not by the more common scenario of spiral magnetism. The experimental findings are corroborated by ab initio calculations of the electric polarization and the underlying spin and orbital order. The results point toward a charge rearrangement due to dimerization, where electronic correlations and the proximity to the insulator-metal transition play an important role.