The developments of satellite communication in network systems require strong and effective security plans. Attacks such as denial of service (DoS) can be detected through the use of machine learning techniques, especially under normal operational conditions. This work aims to provide an interruption detection strategy for Low Earth Orbit (\textsf{LEO}) satellite networks using deep learning algorithms. Both the training, and the testing of the proposed models are carried out with our own communication datasets, created by utilizing a satellite traffic (benign and malicious) that was generated using satellite networks simulation platforms, Omnet++ and Inet. We test different deep learning algorithms including Multi Layer Perceptron (MLP), Convolutional Neural Network (CNN), Recurrent Neural Network (RNN), Gated Recurrent Units (GRU), and Long Short-term Memory (LSTM). Followed by a full analysis and investigation of detection rate in both binary classification, and multi-classes classification that includes different interruption categories such as Distributed DoS (DDoS), Network Jamming, and meteorological disturbances. Simulation results for both classification types surpassed 99.33% in terms of detection rate in scenarios of full network surveillance. However, in more realistic scenarios, the best-recorded performance was 96.12% for the detection of binary traffic and 94.35% for the detection of multi-class traffic with a false positive rate of 3.72%, using a hybrid model that combines MLP and GRU. This Deep Learning approach efficiency calls for the necessity of using machine learning methods to improve security and to give more awareness to search for solutions that facilitate data collection in LEO satellite networks.