The mother and son appear to be outside over a bed of tiny blue flowers, which have been identified as forget-me-nots, aka Princess Diana's favorite flower.
The caption next to the image read: "Paying tribute to all mothers today - past, present, mothers-to-be, and those lost but forever remembered".
The royal, who also met with leukaemia and brain tumor patients, shared that his newborn had kept him awake the previous night, adding that he's still getting used to the idea of being a parent.
The Duke and Duchess of Cambridge visited Archie for the first time today.
But the young princes and princess are hoping they won't have to wait much longer.
William said they were "obviously thrilled, absolutely thrilled" at Archie's birth, and then said he and Kate were "obviously looking forward to seeing them in the next few days when things have quieted down".
She told News.com.au: "The Duke and Duchess of Sussex have decided against letting their son be titled the Earl of Dumbarton, rather he will be known by the more democratic Master".
She said: "It makes ideal sense Harry wants to protect his child from ever being used as a pawn as some part of palace skulduggery".
The minute we saw Prince Harry arrive onto out TV screens after the arrival of his baby son, we just knew he would be the most doting dad ever.