Tanner Higgins Rinaldi, who was born with his right hand missing, caught the prince's eye as he was preparing to take part in the event along with dozens of US soldiers.
The two-year-old put his prosthetic arm up and touched fists with the 25-year-old royal who smiled and laughed.
Harry spent a few minutes chatting to the tot who was held by his mother Debbie before leaving the pair to take his place in the starting line-up.
Mrs Higgins Rinaldi, a personal trainer from Mount Arlington in New Jersey, said after the meeting: "It was absolutely fabulous to meet Harry. I really respect his dedication to the disabled and Armed Forces."
Harry walked the 1.7-mile course of the Achilles Hope and Possibility Run through the leafy groves of Central Park surrounded by the disabled servicemen injured in Iraq and Afghanistan and a large security entourage.
The main event over five miles, which featured disabled competitors who walked, ran and rode "hand cycles", was started by Heather Mills, 42, former wife of Paul McCartney, who lost her left leg below the knee in a road accident and is a campaigner for the disabled.
Harry spent much of the 30 minutes it took him to complete the circuit pushing a quadruple amputee, Corporal Todd Nicely, 26, from St Louis, Missouri.
The serviceman, from 22 Marine Corps, was injured only three months ago when he stepped on an improvised explosive device while on a routine patrol in Afghanistan's Helmand Province.
The corporal said: "It was great having the prince behind me, he was fantastic and we just chatted about what happened to me out in Afghanistan."