The ceremony was conducted by the Archbishop of Canterbury Justin Welby in the castle's Private Chapel, Buckingham Palace said.
In accordance with royal tradition, the Lily Font and water from the River Jordan were used during the christening, and Archie, who was born on May 6, wore the handmade replica of the royal christening robe.
On their official Instagram page, Harry and Meghan, known as the Duke and Duchess of Sussex, shared two official photographs of the occasion taken in the Green Drawing Room and the Rose Garden at Windsor Castle.
One family portrait included Harry's father, Prince Charles, Meghan's mother Doria Ragland as well as Harry's older brother Prince William and his wife, Kate. Harry and William's maternal aunts, Sarah McCorquodale and Jane Fellowes, also posed for the picture.
A second black and white photograph showed Archie in his parents' arms in the Rose Garden.
Buckingham Palace has not disclosed who Archie's godparents are.
Several newspapers have carried reports criticizing Harry and Meghan for accepting public funds for their wedding and for renovations for their new house but denying the public a view of the baby and his parents arriving at the ceremony.
William and Kate organized media facilities for the christenings of their three children, in which arrivals at the church were filmed.
Royal fans gathered near Windsor castle on Saturday, some with banners and flags, despite the well-publicized private nature of the occasion.
"I think it's very hurtful to the fans, very, very hurtful," said Anne Taley, 63, from Cardiff. "We've had the fingers, we've had the toes. When are we ever going to see the baby?" she added referring to previous discreet pictures posted by the royal couple.
Cheryl Bolson, 53, from Southampton, said she accepted the christening was a private, family event but added: "It would be nice if they were to come out afterwards and just maybe show the public that the baby’s been christened."Harry and Meghan married at Windsor Castle, west of London, last year. Archie is seventh-in-line to the British throne.