Typically, you will have to handle the packing for your move yourself. That is, unless you choose full-service professional movers. A good moving company will offer packing services done by expertly-trained crew with delicate care and all of the right supplies.
Any good moving company will provide tailorable services, so if you don’t want packing services, you don’t have to have them. They can pack all of your items, leave all of the packing to you, or just pack some of your items to keep your more fragile or valuable items extra safe.