In this work, we present an optimal control problem under state constraints for breast cancer treatment by chemotherapy. In this instance, the drug dosage is considered as a control variable. Since chemotherapeutic agents affect both tumor cells and healthy cells, the main goal of the control problem is to minimize the evolution of tumor cells with less possible damage to the normal tissue. A system of nonlinear reaction-diffusion equations is used to describe the drug concentration in the tumor cells. The optimal control problem is formulated by specifying a performance criterion and different kinds of constraints, and the necessary optimality conditions are investigated. Afterward, numerical simulations with realistic data are presented and discussed to demonstrate the importance of suggesting optimal control strategies for tumor cell dynamics and eradication. Finally, the conclusion and the future perspectives are presented.