The maximization of biomass productivity in the fed-batch fermentation of Saccharomyces cerevisiae is analyzed. Due to metabolic bottleneck, often attributed to limited oxygen capacity, ethanol is formed when the substrate concentration is above a critical value, which results in a decrease in biomass productivity. Thus, to maximize the production of biomass, the substrate concentration should be kept at the critical value. However, this value is unknown a priori and may change from experiment to experiment. A way to overcome this lack of knowledge is to allow the cells to produce a very small amount of ethanol. This way, the problem of maximizing the production of biomass is converted into that of regulating the concentration of ethanol, for which cell growth can be viewed as a perturbation. A novel adaptive control methodology based on the internal model principle is used to maintain the desired ethanol setpoint and reject the perturbation. Only a single parameter needs to be estimated on-line. Experimental results demonstrate the effectiveness of the proposed control methodology.