An implantable graft, which may be inserted into a fistula tract to occlude the primary opening of the fistula, is provided. To prevent unintentional displacement of the graft or extrusion of the graft from the fistula of a patient, the graft may be provided with a cap that extends laterally from at least one end of the body of the graft, where the cap may be integral with the body of the graft, attachable to at least one end of the body of the graft, and/or moveable along the body of the graft. The graft may also have a tail that extends from one end of the body of the graft to assist in placement of the graft in a fistula tract. The graft may be an integral unit made of a single material, such as a heterograft material, or may include distinct components made of the same or different materials. Methods for closing a fistula tract are also provided.