Last few decades have observed exponential growth in network demands due to increased popularity of real time applications, such as live chat, gaming etc. The resulting infrastructure growth has made it difficult for the service providers to abide by the service level agreements, especially with regards to the quality of service guarantees. Predicting network latencies from noisy and missing measurements has therefore emerged as an important problem, and a plethora of solutions have been proposed for the same. Existing network latency predictions rely either on Euclidean embedding or matrix completion methods. This work considers the estimation and prediction of network latencies from a sequence of noisy and incomplete latency matrices collected over time. An adaptive matrix completion algorithm is proposed that can handle streaming data at low computational complexity. The performance of the proposed algorithm is characterized both in theory and using a real dataset, demonstrating its viability as a network monitoring tool.