Other royal fans were quick to defend William and Kate for the post, praising them for presenting a united front.
"I like this demonstration of unity and family. So important," said one touched user.
"Hey haters - they probably picked it because a bunch of them are together laughing," wrote another.
Harry also took to Instagram to wish his wife and mother of his child Archie Harrison a happy birthday.
Meghan has also received birthday wishes from other royal family members including Queen Elizabeth, Prince Charles and Camilla.
British Vogue Editor in Chief Edward Enniful and her best friend Jessica Mulroney also sent the Duchess birthday wishes.
Last month, Kate Middleton and Meghan Markle put the rumours of a royal feud to bed after they were seen laughing together at Wimbledon, and have only grown closer since the royal wedding, according to new reports.
A source told Hello that "Kate was a great source of support to Meghan in the days leading up to Archie's birth and, despite reports of a rift, they are family and have a really lovely friendship."
The source said Meghan and Kate "talk and text regularly," having more in common since Archie was born.
"Kate has wanted to make sure Meghan has felt welcome into the family," the source added.
Recently, the two royals have been photographed together often, perhaps in an effort to display a united front.