The family is in lockdown in Los Angeles, where they moved at the end of March.
Archie is the fourth royal to mark his birthday in lockdown, and is likely to only see his parents on his big day.
Although Harry and Meghan have been very private about their son, they promised fans a new photo for his birthday on Wednesday.
They shared a video which has been released in partnership with Save the Children UK, and posted on the charity’s Instagram.
In the video, Archie sits on his mom’s lap as she reads Duck! Rabbit!, written by Amy Krouse Rosenthal and illustrated by Tom Lichtenheld.
Archie helps turn the pages and laughs along with the images, which playfully work out whether an animal is a duck or a rabbit.
Behind the camera, Harry can be heard helping to make some animal noises. At one point, Meghan adds her son’s name into the story, saying: “Look Archie, it’s flying!”
She also reveals they shorten his name to Arch.
In a moment many parents will relate to, the young royal is distracted by another book, and pulls it up to his mother — who tells him, “We’ll read that after.”
Archie then proceeds to drop it on the floor twice, prompting Meghan to look at Harry and laugh.
Harry can also be heard cheering behind the camera when they finish reading, and says “Bravo!”
Meghan and Archie are dressed for the warm California climate in the video, with the duchess in shorts, and Archie in a white onesie and diaper.
Meghan has a few bracelets on her right wrist, and her engagement and wedding rings can be spied on her left hand.
A Sussex spokesman said: “As they celebrate this family moment, the duke and duchess wanted to continue to raise awareness around the urgency of bringing food and learning resources to millions of children.
“The duchess chose to read one of Archie’s favorite stories, Duck! Rabbit!”
The video encourages people to donate to the Save the Children stories campaign to support vulnerable families in the U.K.
Meghan joins other famous faces — including Helen Mirren, Jude Law, Stephen Fry and the singers Rita Ora and Liam Payne of One Direction — who have read stories shared online.
Gemma Sherrington, fundraising director at Save the Children UK, said: “Many national education systems already face considerable challenges as a result of conflict and displacement, environmental emergencies and a lack of funding. COVID-19 further compounds these challenges. Countries are under huge pressure in responding to the pandemic, and education budgets risk being reduced.
“We’re delighted that the duke and duchess have chosen to focus attention on the need to protect a generation of children from the consequences of COVID-19.”