We present a framework for safe and optimal trajectory tracking by combining Model Predictive Control and Sampled-Data Control Barrier functions. This framework, which we call Corridor MPC, safely and robustly keeps the state of the system within a corridor that is defined as a permissible error around a reference trajectory. By incorporating Sampled-Data Control Barrier functions into an MPC framework, we guarantee safety for the continuous-time system in the sense of staying within the corridor and practical stability in the sense of converging to the reference trajectory. The proposed framework is evaluated with a free-flyer kinematics system.