The video call comes amid reports of fraught royal relationships, particularly between Harry and his older brother Prince William.
Mr Andersen, who penned the royal book Brothers and Wives: Inside the Private Lives of William, Kate, Harry, and Meghan, said sources informed him of the call.
He said: “From what I understand, they did a video call, they wished her a happy birthday, very private.
“But, Harry and Meghan were not going to post anything as they did two years ago when Kate turned 38.”
Mr Andersen added: “Both Harry and Meghan made a very public display of their affection for Kate at that time.
“This time everything was kept private.”
He then discussed Kate’s birthday celebrations last weekend, which he described as “very low-key”.
The 72-year-old American journalist said: “From what I understand, the birthday was kept to a small family affair.
“It was held an Amner Hall, with family and friends. Kate only has a small circle of friends. They baked their own cakes.”
The low-scale event was in part due to the ongoing COVID pandemic and restrictions.
However, with William turning 40 in June, it is thought that a joint celebration is already in the works for the summer.
While the birthday celebrations were subdued, Kate did publicly mark the milestone by releasing three portraits that served as a nod to the late Princess Diana and the Queen.
Kate also honoured Her Majesty by wearing her Diamond Frame earrings while posing in a red Alexander McQueen gown.
The photographs will be featured at the National Portrait Gallery.
Royal expert Robert Jobson recently noted that Kate and William have been tasked with keeping the monarchy “relevant” as Prince Charles works to “streamline” the family.
Source: EXPRESS CO UK