Bayesian statistical inversion can integrate diverse data sets to infer the posterior probability distributions of subsurface elastic properties. However, certain existing methods may suffer from two issues in practical applications, namely, spatial discontinuities and the uncertainty caused by low-quality seismic traces. These limitations are evident in prestack statistical inversion because some traces in prestack angle gathers may be missing or may be of low quality. We have developed a prestack Bayesian statistical inversion method constrained by reflection features to alleviate these issues. Based on a Bayesian linearized inversion framework, the adopted inversion approach is implemented by integrating the prestack seismic data with reflection features. The reflection features are captured from the poststack seismic profile, and they represent the relationships of the reflection coefficients between different traces. By using our approach, we are able to achieve superior inversion results and to evaluate inversion uncertainty simultaneously even with the low-quality prestack seismic data. The results of the synthetic and field data tests confirm the theoretical and practical effects of the reflection features on improving inversion continuity and accuracy and reducing inversion uncertainty. Moreover, this work gives a novel way to integrate the information of geologic structures in statistical inversion methods. Other geologic information, which can be linearized accurately or approximately, can be used in this manner.