Recently, there has been a significant amount of interest in satellite telemetry anomaly detection (AD) using neural networks (NN). For AD purposes, the current approaches focus on either forecasting or reconstruction of the time series, and they cannot measure the level of reliability or the probability of correct detection. Although the Bayesian neural network (BNN)-based approaches are well known for time series uncertainty estimation, they are computationally intractable. In this paper, we present a tractable approximation for BNN based on the Monte Carlo (MC) dropout method for capturing the uncertainty in the satellite telemetry time series, without sacrificing accuracy. For time series forecasting, we employ an NN, which consists of several Long Short-Term Memory (LSTM) layers followed by various dense layers. We employ the MC dropout inside each LSTM layer and before the dense layers for uncertainty estimation. With the proposed uncertainty region and by utilizing a post-processing filter, we can effectively capture the anomaly points. Numerical results show that our proposed time series AD approach outperforms the existing methods from both prediction accuracy and AD perspectives.