Next, take your vacuum cleaner and use it to suck up more mold from the chair's surface area. Once you're done, throw away the disposable bag of your vacuum immediately. If it's not disposable, then make sure to clean it outside the house.
Leave the chair out in the sun and open air for a day so that the heat dries it thoroughly. If sunny weather is not available, then an electric heater will do fine too. Drying and airing the chair will not allow mold to grow.
There are a few more ways to get rid of mold if it remains or if you prefer trying other methods. Use a soapy sponge, or one with detergent in it, to lightly wipe the chair without letting water be absorbed in it. Then wipe the suds away with a damp cloth.
Another way to clean it is by using an alcohol-moistened cloth (denatured alcohol mixed with water). Make sure to dry your chair properly afterwards.
If the molding is also present on the inside of your chair, then the only option, rather than getting rid of the chair itself, is to contact a disinfection or fumigation service. The local pest control service should also be able to deal with your problem.
To remove the smell from your chair, you can use either charcoal or baking soda, or both. You do this by placing the charcoal, or bowls with baking soda in them, on different parts of the chair. Don't rub them onto the chair. Just let them lie there and they will absorb the odor.