This paper concentrates on the state observation in bioprocesses when there is uncertainty on the process parameters and/or the process inputs. An interval observer is designed on the basis of the cooperativity properties of the model for a standard stirred tank bioreactor model with a single microbial growth and a kinetic model depending on the substrate concentration. Further assumptions are the (lower and upper) boundedness of the specific growth rate and the inlet substrate concentration. Mathematical analysis of the stability and convergence of the interval observer is performed both in absence and in presence of uncertainty on the measurements. It is shown in particular that when the process inputs are known, the static observation error on the unknown state is inversely proportional to one of the observer gains. The performance of the interval observer are also illustrated through numerical simulation.