The incident happened about 1pm at the Coromandel's Ōtama Beach, on Wednesday, a day after the family had gathered together to welcome the start of 2019.
Wright, of Auckland, ran to grab his cell phone to get a snap of the shark - which he guessed was at least 2m long.
"It looks small in the footage...but it was a flippin' big shark and it was in waist-deep water when we looked out.
"Right in front of us, it turns around and comes towards us while we're standing on this rock and turns around and goes out towards the beach."
Wright said despite the somewhat scare of being near a shark, it brought a lot of excitement for the children among the party - including his daughter Hollie, 15, and 9-year-old son Jackson.
"It was a huge thrill for my son, Jackson, as he is obsessed with sharks and often wears a shark tooth necklace he got from Fiji.
"I had just told them not to worry because there wouldn't be any sharks there,'' he laughed.