Make sure the fabric on the chairs is dry. Put them in a warm and sunny space to get rid of any dampness before starting to clean them.
Brush the dry mold off of the fabric with a stiff brush, as the University of Illinois Extension suggests. Removing as much of the mold as possible before washing the fabric helps prevent stains and prevent the mold spores from spreading.
Wash the moldy spots thoroughly with soap and water. Use a mold cleaner that contains bleach on white fabrics, but do not use bleach on colored fabrics that the bleach will stain.
Place the chairs in a hot and sunny area to dry. Drying them right away helps prevent mold. It helps kill old mold spores and eliminate the damp fabric environment that contributed to mold growth in the first place.
Spray a fungicide on the fabric, if desired. Fungicide helps kill the mold spores and prevent the mold from returning, but fungicide can contain irritating chemicals. The University of Missouri Extension recommends using fungicides on fabrics before storing them for extended periods of time. People who store outdoor fabric chairs in a damp garage or basement during the winter should consider spraying a textile fungicide once per year before putting them in storage.
Spray the chairs with a water repellent, as the University of Missouri Extension recommends to prevent mold on fabrics.