To be allowed in the washing machine, upholstery fabrics have to pass 2 tests. They must be pre-shrunk and they must be colorfast.
To find out if your upholstery is pre-shrunk, the best place to look is a manufacturer's tag. If your upholstery is not pre-shrunk, washing in the washing machine will shrink the fabric and make it difficult to impossible to have the item fit back where it belongs.
To find out if your upholstery is colorfast, take a damp white cloth and rub it on the upholstered surface. If color comes off onto the cloth, the upholstery is likely not colorfast and a professional will need to handle the cleaning of your furniture.