In this paper, the concepts of metric space in the parlance of Soft Set Theory have been introduced in crisp and fuzzy sense. Moreover, we have also defined various types of fuzzy soft metric spaces as Strong Fuzzy Soft Metric Space, Fuzzy Soft Product Metric Space and their properties as Diameter of a Fuzzy Soft Set (FSS), Distance between two FSS and related theorems have been proposed. All these definitions have been discussed by taking appropriate examples.