Cut off the burned edges of the burn with manicure scissors or very small, fine scissors. When a burn occurs, the burned edges crinkle upward slightly, and these edges can be removed with the scissors so that all that is left is the burn mark or small hole. Even if your burn just left small microfiber frays and not a bigger hole, cut away those frays.
Apply fabric glue to a toothpick or small brush and brush the edge of the burn hole. This will prevent the fabric from fraying.
Ask the sofa manufacturer for a sample of the fabric. If the manufacturer cannot give you a sample of the fabric, try to match the fabric of the sofa to one that you can purchase in a fabric store. If no samples are available in a fabric store, you can cut a small piece of the sofa fabric from your sofa, such as on a pillow, the bottom or back of the sofa that is hidden from view. You will need to cut a piece of fabric that is about 25 percent bigger than the hole, fray or mark. For leather sofas, you may be able to purchase a leather repair kit that contains this leather sample that will match your sofa
Apply fabric glue to the outer edge of the fabric sample.
Push the fabric sample carefully into the hole or fray and then use tweezers to position the fabric so that it fills in the hole and matches any pattern on the sofa.
Lay a piece of plastic wrap on top of the repaired burn hole or fray, then place a book or weight on top of it and wait several hours for the glue to dry.