Photogenerated carrier dynamics in an AlGaN/GaN single quantum well has been studied using a conventional degenerate pump and probe technique at room temperature. Photoinduced absorption at the exciton resonance has been observed. It is explained by the absorption coefficient change, through the quantum-confined Stark effect and the quantum-confined Franz-Keldish effect, caused by the photoinduced internal electric-field screening. In comparison with biased GaAs multiple quantum wells, a slower time evolution of differential transmission signals has been also found. Its origin is attributed to the longer carrier sweep-out time due to the potential profile of the sample in conjunction with the longer carrier recombination time.