Trim any frayed material or threads from the burned fabric with nail scissors. Smooth the fabric in the burned area, even if there are some missing spots.
Use a handheld vacuum to clean the seat around the burned area. Vacuuming the seat will pick up leftover ash so that it will not not stain other sections of the seat.
Pour one drop of mild face soap onto a damp rag. Dab the rag over the burned area without rubbing it in. Use a blotting motion to pick up the residue from the burn.
Wait for the dampened area on the seat to dry. Vacuum it again to ensure that any excess residue is picked up.
Apply a dab of epoxy to a flat wooden stick and spread it thinly over the cigarette burn. This clear coat will seal the edges of the fabric, ensuring that they will not fray.
Cover the cigarette burn with a piece of corresponding fabric. Cut a scrap of fabric that is just large enough to cover the burn. Apply fabric glue to the backside of the fabric, and place it glue-side down onto the burn. Hold the fabric in place for 30 seconds and release the pressure. Allow the glue to dry thoroughly before using the chair.