It obviously matters on the person and what the goals are.
If the goal is to ultimately break two hours for the marathon because perhaps the child's parents were quite successful, my opinion is that too young is probably 23 years old.
If the concern is physical danger to the kid, such as stunting his or her growth or damaging his or her heart, I think five or six years old is too young. Really. I ran several marathons at age eight and my brother ran several at age six. We both continued running marathons past ten years old. I think I had run 25 marathons by age 12. My brother then took up soccer and forgot about running. I have not stopped running and I'm now 45.
I grew just fine, as did my brother, but at the time a few people whispered that our growth might be stunted. Remember, back in the early to mid-70's there were tons of kids (yes, kids) running marathons. Kevin Strain from Alaska, Tom Ansberry (yes of 28 min 10K PR ran 2:43 at age 13 at Mission Bay Marathon in about 1975), Mary Etta Boitano, Reggie Heywood of Arizona (2:57 at age 10), Dutch Workman, Daven Chun and the "Hunky Bunch" out of Hawaii.
At Palos Verdes Marathon in 1976, there must have been 30 kids under 12 who finished. One 12 year named Mike Marckx ran 2:49 and later ran 14:30 for 5K as an adult.
My brother and I are both healthy in every respect. My 400 meter speed may have been a little slower in high school and college than had I not run such long distances (even a 50 mile race at age 10), but I don't know.
I don't want to sound like some Gallowalker, but the important thing in my mind in considering if your child should run a marathon is consideration of what mental benefits of it - goal setting, discipline, learning to suffer, being competitive, tenacity - and how running simply as a sport is great. The physical concerns are probably way overblown.
If the concern is mental issues, I think the key is just never pushing them. My parents never pushed me at all. I never burned out. I never had a coach until high school, although I read almost every page of Runner's World back then, as well as every book on running I could get my hands on. I read Lydiard, but I didn't understand him like I do now.
If my ten year old, nine year old or seven year old kids wanted to run a marathon, I would very gently encourage them, but it would have to be their own initiative to do so.
Of the kids I ran marathons with and trained with in the mid-70's, two went on to Stanford, another to Harvard, another to Pomona College. Another became a professional triathlete. I think running long distances lends itself to becoming an over-achiever of sorts, which can be good.