In the short clip Miss Piggy rushes up to Kermit and exclaims: "Isn't it exciting Kate is a mommy, Prince William is a daddy and there's a new royal baby boy."
"Yeah it's wonderful," he replies, slightly less enthused his friend.
Then his porcine companion suggests that Kermit might be feeling broody for some tadpoles of his own.
"Kind of makes you want to have a royal child of your own, doesn't it?" she asks. "Can't you just hear the little pitter patter tadpole feet."
"Tadpoles don't have feet," he shoots back – at which Miss Piggy says: "You really know how to kill a beautiful moment, don't you?"
The video was made in London where their new movie Muppets Most Wanted starring Tina Fey, Ricky Gervais and Tom Hiddleston is being shot. The Muppets weren't the only celebrities to send their congratulations.
Ellen DeGeneres, who was recently informed by the New England Genealogical Society that she is a distant relative of the future Queen, tweeted her delight.
"It's a boy! So happy for my cousin Kate and the future King of England," said the chat show host.
Michelle and Barack Obama sent a message to William and Kate congratulating them "on the joyous occasion of the birth of their first child." They added: "We wish them all the happiness and blessings parenthood brings. The child enters the world at a time of promise and opportunity for our two nations."
"Given the special relationship between us, the American people are pleased to join with the people of the United Kingdom as they celebrate the birth of the young prince."