The article proposes a nonlinear optimal control approach for the dynamic model of the acute inflammatory response. This model describes the reaction of the human body to bacterial infection. Optimal control of the infusion of anti-inflammatory and anti-bacterial medication is critical for achieving more effective and less costly pharmaceutical treatments. To solve the related nonlinear optimal control problem the state-space description of the acute inflammatory response undergoes first approximate linearization around a temporary operating point which is recomputed at each iteration of the control algorithm. The linearization relies on Taylor series expansion and on the computation of the associated Jacobian matrices. For the approximately linearized model of the acute inflammatory response a stabilizing H-infinity feedback controller is designed. This controller stands for the solution of the optimal control problem under model uncertainties and external perturbations. To find the controller's feedback gains an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control scheme are proven through Lyapunov analysis.