The 'Rocket Man' singer expressed concern that Zachary, who was born via a surrogate on Christmas Day 2010, will be victimised due to his celebrity status and homophobia in the playground.
"Being the child of someone famous is a huge ball and chain around your ankles. It's going to be very difficult," he told the Radio Times.
"At school other children will say, 'You don't have a mummy'. We've come a long way, but there's still homophobia and will be until a new generation of parents don't instil it in their children."
John stated last month that he would "definitely" like to have another child.
"[Fatherhood] changes everybody," he said. "It's the most wonderful thing you can go through. I regretted that I didn't do it sooner, but he's changed our lives."