The proper classification of plasma regions in near-Earth space is crucial to perform unambiguous statistical studies of fundamental plasma processes such as shocks, magnetic reconnection, waves and turbulence, jets and their combinations. The majority of available studies have been performed by using human-driven methods, such as visual data selection or the application of predefined thresholds to different observable plasma quantities. While human-driven methods have allowed performing many statistical studies, these methods are often time-consuming and can introduce important biases. On the other hand, the recent availability of large, high-quality spacecraft databases, together with major advances in machine-learning algorithms, can now allow meaningful applications of machine learning to in-situ plasma data. In this study, we apply the fully convolutional neural network (FCN) deep machine-leaning algorithm to the recent Magnetospheric Multi Scale (MMS) mission data in order to classify ten key plasma regions in near-Earth space for the period 2016-2019. For this purpose, we use available intervals of time series for each such plasma region, which were labeled by using human-driven selective downlink applied to MMS burst data. We discuss several quantitative parameters to assess the accuracy of both methods. Our results indicate that the FCN method is reliable to accurately classify labeled time series data since it takes into account the dynamical features of the plasma data in each region. We also present good accuracy of the FCN method when applied to unlabeled MMS data. Finally, we show how this method used on MMS data can be extended to data from the Cluster mission, indicating that such method can be successfully applied to any in situ spacecraft plasma database.