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) can exploit the causal relationships between the system variables and sequentially perform 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. We first derive a graphical characterization for potentially optimal sets of variables to intervene upon. Showing that any MO-CBO problem can be decomposed into several traditional multi-objective optimization tasks, we then introduce an algorithm that sequentially balances exploration across these tasks using relative hypervolume improvement. The proposed method will be validated on both synthetic and real-world causal graphs, demonstrating its superiority over traditional (non-causal) multi-objective Bayesian optimization in settings where causal information is available.