Dynamic movement primitives are widely used for learning skills that can be demonstrated to a robot by a skilled human or controller. While their generalization capabilities and simple formulation make them very appealing to use, they possess no strong guarantees to satisfy operational safety constraints for a task. We present constrained dynamic movement primitives (CDMPs), which can allow for positional constraint satisfaction in the robot workspace. Our method solves a non-linear optimization to perturb an existing DMP's forcing weights to admit a Zeroing Barrier Function (ZBF), which certifies positional workspace constraint satisfaction. We demonstrate our approach under different positional constraints on the end-effector movement on multiple physical robots, such as obstacle avoidance and workspace limitations.