Cyber-physical systems are engineered systems that rely on the integration of physical processes and computational resources. While this integration enables advanced techniques for monitoring and controlling systems, it also exposes the physical process to cyber-threats. An attacker who is able to access control inputs and mask measurements could damage the system while remaining undetected. By masking certain measurement signals, an attacker may be able to render a portion of the state space unobservable, meaning that it is impossible to estimate or infer the value of those states. This is called an observability attack. A game-theoretic approach is presented to analyze observability attacks. The attacker's strategy set includes all possible combinations of masked measurements. The defender's strategy set includes all possible combinations of measurement reinforcements. The attacker's and defender's utilities are quantified using the responses of the observable and unobservable states. The observability attack game is analyzed for a nuclear balance of plant system. Multiple pure-strategy and mixed-strategy Nash equilibria are identified, and the conditions for their existence are presented. Using this procedure, a security and control engineer can select the optimal strategy to defend a cyber-physical system from observability attacks.