The above answers are absolutely right and I will echo it again, it is about the child understanding that they will have to take up that responsibility to ensure their hygiene is up to standard and that they are able to effectively manage and care for the lenses. We see children as young as 6 who are able to proficiently manage lenses although we always want the parents to be involved in some way to ensure they are doing things the right way. This can be followed through until they have proven to be responsible to manage it on their own.
Like what Yuna mentioned, it is more a matter of whether your child is able to take up the responsibility of wearing contacts. I have a couple of friends who allowed their children (at teenage age) to wear contacts as their children play sports and it is more convenient to wear contacts rather than spectacles.
I read that on average, people can start wearing contacts from 12, but it has been shown that some younger children are mature enough to wear and care for contact lenses. Reckon that wearing contacts is more about responsibility than age. I started wearing contacts at 10.