In decision-making problems, the outcome of an intervention often depends on the causal relationships between system components and is highly costly to evaluate. In such settings, causal Bayesian optimization (CBO) exploits the causal relationships between the system variables and sequentially performs interventions to approach the optimum with minimal data. Extending CBO to the multi-outcome setting, we propose *multi-objective Causal Bayesian optimization* (MO-CBO), a paradigm for identifying Pareto-optimal interventions within a known multi-target causal graph. Our methodology first reduces the search space by discarding sub-optimal interventions based on the structure of the given causal graph. We further show that any MO-CBO problem can be decomposed into several traditional multi-objective optimization tasks. Our proposed MO-CBO algorithm is designed to identify Pareto-optimal interventions by iteratively exploring these underlying tasks, guided by relative hypervolume improvement. Experiments on synthetic and real-world causal graphs demonstrate the superiority of our approach over non-causal multi-objective Bayesian optimization in settings where causal information is available.