Carter said his father was his "mentor & has always been there for me".
He posted a photograph on Instagram of his father when he received his cap for his 100th All Blacks test.
Hollie Smith also posted on Instagram, simply captioning her family photo "Dad day".
Real Housewives of Auckland star Gilda Kirkpatrick also took to Instagram to share a family snap and Father's Day message.
Labour leader Jacinda Ardern posted about her father Ross on Facebook.
"Happy Father's Day to the one who taught me how to ride a bike, change a tyre, give a speech, and dance," she wrote.
"Couldn't ask for one better."
All Black Sonny Bill Williams posted a sweet photograph of him with his little girls Imaan and Aisha.
The rugby star spenthis morning surrounded by Play-Doh.
The All Blacks tweeted a photograph of Ben Smith and his adorable daughter at a recent Bledisloe Cup match.
"Happy #FathersDay to all the dads out there from the All Blacks," they posted.
"We hope you have a wonderful day."
At the home of The Hits and Seven Sharp host Toni Street, Father's Day wasn't quite going to plan.
The mum-of-two posted a photograph of a special breakfast on a tray, which appears to have been dropped on the floor soon after.
Actor and presenter Jaquie Brown seemed to be having similar bad luck, posting on Twitter that her child had taken to a wall with a pen to mark Father's Day.
Former model and social media regular Anna Reeve posted a touching tribute to her husband Jay Reeve, father to twins Oscar and Hunter.
"From the very start @thejayreeve has been the most caring partner and incredible father," she wrote on Instagram.
"That's what defines you as an amazing father to me Jay, you're steady in bringing your infectious zest for life and love to all the peaks and valleys of this crazy parenthood ride.
"We are lucky to call you all ours."