Depending on the place you go kids can ride ziplines even as young as 3. They won’t be able to ride alone as their weight won’t give them the momentum they need to make it all the way across on the long lines. A minimum of weight is usually in place of around 60 or 70 pounds. The smaller children will usually be tethered to mom, dad or another adult. The zipline tour guides are also able and more than willing to accompany the little one on their zip line adventure.
The places near me in Gatlinburg and Pigeon Forge, Tennessee charge the same price for child and adult tickets so you might find this to be the industry norm. After watching a couple zip line videos I noticed that both riders, the adult and child each had separate gear, trolleys and harnesses. They were tethered by a strap.
Keep in mind that zipline tours often involve several lines that can take the child out of the parent’s view so it’s required that an older adult accompany them throughout the tour. The age minimum that I have found is usually no less than 16 years old.