According to DoItYourself, felt material can be cleaned either by hand or in a washing machine. Although machine washing felt material is easier and less time consuming, this method is more likely to damage the fabric. Hand washing felt is the safest way to ensure that the material stays in good condition.
To hand wash felt material, begin by letting the piece soak in a mixture of cold water and mild laundry detergent. Let the fabric soak for a few minutes, and then remove the item and knead the fabric gently by hand. Alternatively, a soft-bristled brush can be used on the felt, but this method can damage the fabric if not applied gently. After massaging the material, wring the item out, and lay it out on a clean surface to dry, preferably on top of a towel.
To machine wash felt material, set the washing machine to use only cold water and the gentlest cycle possible. Let the machine fill with water, and add fabric softener and a gentle detergent before adding the felt item. Felt clothing can be washed along with other clothes as long as the machine is set to cold water and a delicate cycle. After the piece is washed, lay the fabric out on a flat surface and allow it to air dry. Using a heated dry causes the material to distort.