Human-robot collaboration (HRC) in manufacturing environments requires that physical safety can be guaranteed. Control methods that implicitly regulate the interaction forces between a controlled robot and its environment, such as impedance control, are often used for safety in HRC. However, these methods could be complemented by restricting the robot operational space for additional safety guarantees. In this context, obstacle avoidance might benefit from considering a prediction of the controlled-robot motion and/or the behavior of the human collaborator. To this end, we proposed to include linearized Safety Control Barrier Functions (SCBFs) in a linear Model Predictive Control (MPC) strategy for robot impedance variation online. The convex optimization problem that was obtained from our proposal presented two advantages compared to nonlinear MPC alternatives. First, optimality was ensured in our method under linearity assumptions on human guidance and linearized robot dynamics, whereas a controller synthesized by nonlinear MPC strategies would depend on the fundamental characteristics of the problem. Second, our method enabled implementation at a faster control frequency, thus allowing a rapid adaptation to changes occurring in the robot environment. Finally, experimental validation was performed using a Franka Emika Panda robot in a human-robot collaborative scenario, and the stability of the method was shown using Lyapunov theory.