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.
He spent a few minutes chatting to the boy, 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: "It was absolutely fabulous to meet Harry. I really respect his dedication to the disabled and Armed Forces."