Tree covering number (T(G)) for a crisp graph G, which is the minimum number of simple trees those are not have common vertices, appear as induced subgraphs for covering up all vertices of the crisp graph G. The main objective of the theoretical portion of this article is to define a fuzzy tree covering number for fuzzy graphs using edge membership and vertex membership functions. The newly defined parameter tread as an effective fuzzy mathematical tool, which is more fruitful and valuable for solving real-life problems with uncertainties. Also, some bounds together with specific characterizations for fuzzy tree covering number are established in this article. In the last part of this article, the electricity distribution system is taken to reflect the realistic applicability of fuzzy tree covering number for fuzzy graphs along with many related results.