A novel extremum seeking scheme is proposed for the optimization of the specific growth rate in fed-batch processes with substrate inhibited kinetics. The proposed controller is based on a high order sliding mode algorithm, which uses the gradient of the specific growth rate as switching coordinate. A gradient estimation is obtained through a high order sliding mode observer. Both the control and gradient estimation algorithms are finite-time stable. The stability of the controller is analysed using Lyapunov functions for both the unperturbed and perturbed cases and guidelines for the algorithm tuning are provided. The controller and observer algorithms are numerically assessed and simulation results are obtained for a set of different scenarios.