There are a number of factors to consider when deciding whether your child should sleep on a memory foam mattress. Most important of all is age. If your child is under two then they should definitely not sleep on a memory foam mattress. This is because the very qualities that make memory foam mattresses so fantastic for adults can actually be quite dangerous for children under two. Memory foam shapes itself to your body, reacting to the heat you emit. While this is great for adults, it can envelope and smother young children, meaning they have trouble turning over and may not be able to breathe.
Another thing to consider is the cost of the mattress versus the risk of it getting soiled. If your child is prone to night time accidents, then you probably should wait to get them a memory foam mattress as it is not something you will want to replace because of damage. Although memory foam is reasonably resilient to spoilage, they are not something you want to have to keep replacing.
By the time your child is about five or six is a good time to consider getting them a memory foam mattress.