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This paper addresses the feature selection problems in the setting of online learning of data streams. Typically this setting imposes restrictions on computational resources (memory, processing) as well as storage capacity, since instances of streaming data arrive with high speed and with no possibility to store data for later offline processing. Feature selection can be particularly beneficial here to selectively process parts of the data by reducing the data dimensionality. However selecting a subset of features may lead to permanently ruling out the possibilities of using discarded dimensions. This will cause a problem in the cases of feature drift in which data importance on individual dimensions changes with time. This paper proposes a new method of online feature selection to deal with drifting features in non-stationary data streams. The core of the proposed method lies in deep reconstruction networks that are continuously updated with incoming data instances. These networks can be used to not only detect the point of change with feature drift but also dynamically rank the importance of features for feature selection in an online manner. The efficacy of our work has been demonstrated by the results of experiments based on the MNIST database.