Summary Finite element (FE) model updating is essential to improve the reliability of physical model‐based approaches in structural engineering applications. The surrogate model is considered an alternative to time‐consuming iterative FE analyses in performing the updating procedure. This paper presents a Bayesian neural network (BNN) as the surrogate model for probabilistic FE model updating using the measured modal data. The BNN involves high computational efficiency by introducing the approximate Gaussian inference of the posterior distribution. In practice, the modal data are usually incomplete because of the measurement noise and limited sensors. The developed BNN exploits the nonlinear relationship between the selected parameters and incomplete modal data. As opposed to the traditional surrogate‐based approach, the proposed framework uses the modal data as inputs and structural parameters to be updated as outputs. It enables uncertainty quantification of the estimated structural parameters efficiently. In particular, an adaptive sampling strategy is established to shrink the searching space of optimal updating parameters based on the truncated Gaussian distribution. Numerical examples are conducted to demonstrate the effectiveness of the presented approach. Then it is applied to the laboratory and experimental structures using the measured data. Results indicate that the proposed framework is accurate and efficient for parameter uncertainty quantification in structural model updating.