COBRA-PPM is a novel causal Bayesian inference architecture that combines causal Bayesian networks and probabilistic programming to perform interventional inference for robotic manipulation under uncertainty. Its performance is demonstrated through Gazebo-based experiments, predicting manipulation outcomes with high accuracy (prediction accuracy: 88.6%) in a block stacking task and performing greedy next-best action selection with a task success rate of 94.2%. We also demonstrate sim2real transfer on a domestic robot, demonstrating its effectiveness in handling real-world uncertainties arising from sensor noise and probabilistic behavior. This generalizable and scalable framework supports a wide range of manipulation scenarios and lays the foundation for future research at the intersection of robotics and causality.