This work proposes a moving target defense (MTD) strategy to detect coordinated cyber-physical attacks (CCPAs) against power grids. The main idea of the proposed approach is to invalidate the knowledge that the attackers use to mask the effects of their physical attack by actively perturbing the grid's transmission line reactances via distributed flexible AC transmission system (D-FACTS) devices. The proposed MTD design consists of two parts. First, we identify the subset of links for D-FACTS device deployment that enables the defender to detect CCPAs against any link in the system. Then, in order to minimize the defense cost during the system's operational time, we formulate a zero-sum game to identify the best subset of links to perturb (which will provide adequate protection) against a strategic attacker. The Nash equilibrium robust solution is computed via exponential weights, which does not require complete knowledge of the game but only the observed payoff at each iteration. Extensive simulations performed using the MATPOWER simulator on IEEE bus systems verify the effectiveness of our approach in detecting CCPAs and reducing the operator's defense cost.