In this paper, the sensor fault detection (FD) problem is investigated for the dynamic point‐the‐bit rotary steerable system (DPRSS), which is known as state‐of‐the‐art oil drilling equipment. Firstly, the DPRSS dynamic is modelled as a linear system with drilling disturbances, which consists of model perturbations, measurement disturbances, and unknown inputs. Secondly, the finite‐frequency H−/H∞${H_ - }/{H_\infty }$ unknown input observer is proposed to generate the residual, which is sensitive to sensor faults and robust against drilling disturbances. Subsequently, considering model perturbations and measurement disturbances, the zonotope‐based residual evaluation method is presented, and the FD decision‐making logic is designed based on the calculated residual bounds. Finally, numerical simulations and prototype experiments are provided to illustrate the effectiveness of the proposed sensor FD mechanism.