Recovery of missing network monitoring data is of great significance for network operation and maintenance tasks such as anomaly detection and traffic prediction. To exploit historical data for more accurate missing data recovery, some recent studies combine the data together as a tensor to learn more features. However, the need of performing high cost data decomposition compromises their speed and accuracy, which makes them difficult to track dynamic features from streaming monitoring data. To ensure fast and accurate recovery of network monitoring data, this paper proposes NMMF-Stream, a stream-processing scheme with a context extraction module and a generation module. To achieve fast feature extraction and missing data filling with a low sampling rate, we propose several novel techniques, including the context extraction based on both positive and negative monitoring data, context validation via measuring the Pointwise Mutual Information, GRU-based temporal feature learning and memorization, and a new composite loss function to guide the fast and accurate data filling. We have done extensive experiments using two real network traffic monitoring data sets and one network latency data set. The experimental results demonstrate that, compared with three baselines, NMMF-Stream can fill the newly arrived monitoring data very quickly with much higher accuracy.