Harry, addressing the audience at the Invictus Games opening ceremony in The Hague, Netherlands, said Archie has expressed an interest in becoming a pilot, with the duke joking that he obviously means a helicopter pilot.
Harry served in Afghanistan as an Apache helicopter co-pilot gunner during 2012-13.
Harry spoke to the crowd – which included former and serving military personnel taking part in the games – about role models and the importance of “character”.
He said: “To be role models, or the role models, that each of you are takes strength and it takes courage.
“When I talk to my son Archie about what he wants to be when he grows up, some days it’s an astronaut, other days it’s a pilot – a helicopter pilot obviously. Or Kwazii from Octonauts. If you’re laughing then you’ve seen that.
“But what I remind him is that no matter what you want to be when you grow up, it’s your character that matters most, and nothing would make his mum and me prouder than to see him have the character of what we see before us today.”
Harry said those involved with Invictus have “overcome immense challenges”, adding: “And together you are healing and teaching the world as you go.”
The duke always dreamed of a life in the Army, and as a child his bedroom was filled with pictures of tanks and helicopters.
In 1993, as an eight-year-old, he was in his element when dressed in a miniature combat suit and helmet to ride in a tank on a visit to Germany.
He joined the Royal Military Academy Sandhurst in 2005, and trained as an Army officer, then joined the Blues and Royals and went on to train to become a troop leader of an armoured reconnaissance unit.
A planned tour to Iraq was scrapped after it was found he would be a target for insurgents, but two tours to Afghanistan followed including one as an Apache helicopter pilot.