Mobile Edge Computing (MEC) and Information-Centric Networking (ICN) are essential network architectures for the future Internet. The advantages of MEC and ICN such as computation and storage capabilities at the edge of the network, in-network caching and named-data communication paradigm can greatly improve the quality of video streaming applications. However, the packet loss in wireless network environments still affects the video streaming performance and the existing loss recovery approaches in ICN does not exploit the capabilities of MEC. This paper proposes a Deep Learning based Loss Recovery Mechanism (DL-LRM) for video streaming over MEC based ICN. Different with existing approaches, the Forward Error Correction (FEC) packets are generated at the edge of the network, which dramatically reduces the workload of core network and backhaul. By monitoring network states, our proposed DL-LRM controls the FEC request rate by deep reinforcement learning algorithm. Considering the characteristics of video streaming and MEC, in this paper we develop content caching detection and fast retransmission algorithm to effectively utilize resources of MEC. Experimental results demonstrate that the DL-LRM is able to adaptively adjust and control the FEC request rate and achieve better video quality than the existing approaches.