Mullite reinforced by SiC whiskers, Mullite(W), was developed with the aim of improving fracture toughness and to add crack-healing ability. For determining the threshold stress during crack-healing, a composite having a semi-elliptical surface crack of 100 μm was crack-healed at 1473 K for 8 h in air under elevated static and cyclic stresses and the bending strength at 1473 K of the crack-healed composite under stress were also investigated. Mullite(W) crack-healed under static stress below 100 MPa were never fractured during crack-healing and had the same bending strength as the specimens crack-healed under no-stress. Therefore, the threshold static stress during crack-healing of Mullite(W) has been determined to be 100 MPa. The threshold cyclic stress has also been determined to be 150 MPa. Considering that the crack growth is time-dependent, the threshold stress for all conditions during crack-healing of Mullite(W) has been concluded to be 100 MPa.