The power laws of network geometric properties are widely adopted to characterize the critical phenomena of complex systems, which may not describe the diverse interactions in systems effectively. By comparison, the causality represents the complicated interactions. Therefore, in this work, the power law of the causal effects in systems is studied to reflect the critical states from the perspective of causality. The causal Bayesian networks and effective information are adopted to construct the causal relationships and quantify the causal effects. The study on 20 systems from different fields shows that for a considerable proportion of systems, the causal effects of the factors in systems follow the power laws. For such causal power laws, an explanation based on the principle of maximum entropy is proposed and verified. The causal power laws may imply some critical states of systems, and can provide the basis for the quantification of systems' states and functions.